Wayne Routledge scored a stunning equaliser as Swansea stopped a run of three defeats and denied Reading their first Premier League win of the season.
A string of top-class saves from Alex McCarthy kept Swansea at bay after Pavel Pogrebnyak squeezed his shot under Michel Vorm to put Reading ahead.
Noel Hunt doubled the visitors' lead with a sharp volley but Miguel Michu's diving header gave Swansea hope.
Steve BowerBBC Match of the Day commentator
"Honours even at the Liberty Stadium. Michael Laudrup's winless run continues but it's a point having been two goals down. Wayne Routledge in the end was the one to get the point with the equaliser after Reading had led 2-0. They still await their first Premier League victory but it's a third point for Brian McDermott's team in an entertaining affair."
The excellent Routledge then hit a pile-driver to claim a draw.
The last time the two sides met was in the 2011 Championship play-off final, when Swansea crushed Reading's Premier League hopes with a
thrilling 4-2 win.
Brian McDermott's side had to wait another season to join their conquerors in the top flight, but Saturday's performance will have given further encouragement despite the disappointment of watching a first win slip from their grasp.
The home side continued to press and Reading goalkeeper McCarthy again had to be on his toes to tip Danny Graham's powerful header over the crossbar, after Routledge whipped in a left-wing cross.
Routledge was again involved soon after as the winger took Michu's pin-point diagonal through ball in his stride but fired straight at McCarthy.
Swansea comeback pleases Laudrup
While it was Swansea's attacking midfielders who were catching the eye, the fulcrum of their neat play was Leon Britton - playing his 400th game for the south Wales club through all four divisions and slotting into the holding role vacated by Joe Allen's departure to Liverpool.
Reading were struggling to get to grips with the game and only the imposing figure of Pogrebnyak offered any relief for the hard-pressed Royals, as the striker used his strength to hold the ball up.
The Russian's appetite for hard-work was rewarded as he gave Reading the lead completely against the run of play, taking Jobi McAnuff's pass down the left channel and watching his shot squirt under Vorm and into the Swansea goal.
The set-back left the usually rock-solid Dutch keeper scratching his head and visibly took the wind out of the sails of a Swansea side who had not found the back of the net in their three previous Premier League games, all defeats.
Reading then delivered a hammer blow a minute before half-time as Hunt doubled the visitors' lead with their second shot on target.
Swansea v Reading facts
Pavel Pogrebnyak's goal was Reading's 100th in Premier League history - the Russian has scored eight goals from just 11 shots on target in the Premier League.
Swansea's Miguel Michu has scored five goals from just seven shots on target this season.
Swansea have won four and lost none of the last seven meetings in all competitions with Reading.
Reading have won just two of their last 23 Premier League away games (W2 D6 L15).
This is the first time Swansea have gone five games without a victory since they returned to the top flight.
Swansea's defence did well to close down a series of snap-shots, but the last from McAnuff spun wickedly off Angel Rangel's foot and dropped perfectly for Hunt who converted with a crisp right-foot volley across Vorm.
Luke Moore replaced Graham for Swansea at the start of the second half and almost made an immediate impact as he surged through the middle, only for McCarthy to pull off a fine save with his outstretched right boot.
Moments later McCarthy again came to Reading's rescue as the goalkeeper clawed Moore's header out of the air and just diverted the ball onto a post.
McCarthy's superb afternoon continued as the keeper instinctively stuck out a hand to parry Ki Sung-Yeung's deflected shot, then saved low to his right to keep out Williams' header from the resulting corner.
Reading's resistance was finally broken 17 minutes from time as Routledge's cross took a slight deflection and Michu flew in at the back post to send a diving header into the net.
Swansea surged foward and within seven minutes Routledge got the goal his efforts deserved, exchanging passes with Moore before smashing home an unstoppable equaliser.
McDermott happy with 'good point'
Pablo Hernandez, on for Nathan Dyer, almost gives Swansea an improbable victory, chipping over the bar amid claims of handball against Nicky Shorey.
But Reading were not finished either and Williams had to be alert to head Jem Karacan's looping header off the line after Vorm failed to get enough distance with a clearing punch.
"I think when you're 2-0 down and come back you should be pleased and then you add we had three consecutive defeats.
"It is important that we stopped the losses. That was important, you can say one point from four is quite poor but we are still five clear of the bottom [three].
"These are the games that show if your team has character and I think we showed that today."
Reading manager Brian McDermott
"I don't look at it like that [waiting for the win to come], I just look at the performances.
"The wins will come with the performances, our belief and confidence is absolutely fine.
"We won the Championship last year, they know how to win games and they will do in this league."
Corner taken by Nicky Shorey, Header from deep inside the penalty area by Hal Robson-Kanu goes harmlessly over the crossbar.
Effort on goal by Jonathan de Guzman from deep inside the penalty area misses to the right of the target.
Jimmy Kebe produces a right-footed shot from deep inside the penalty box which goes wide of the left-hand upright.
Adam Le Fondre takes a shot. Save by Michel Vorm.
Jem Karacan takes a shot. Ashley Williams manages to make a clearance. Corner taken by Nicky Shorey, Sung-Yeung Ki manages to make a clearance.
Substitution Hal Robson-Kanu replaces Jay Tabb.
Shot from just outside the area by Jonathan de Guzman misses to the left of the target.
Chico takes a shot. Kaspars Gorkss gets a block in.
Sung-Yeung Ki takes a shot. Adrian Mariappa gets a block in.
Substitution Jonathan de Guzman is brought on as a substitute for Miguel Michu.
Pablo Hernandez takes a shot. Blocked by Nicky Shorey. Pablo Hernandez produces a right-footed shot from inside the area that clears the crossbar.
Sung-Yeung Ki takes the outswinging corner, save made by Alex McCarthy.
Substitution Adam Le Fondre joins the action as a substitute, replacing Pavel Pogrebnyak.
Assist on the goal came from Luke Moore.
77:16 Goal scored
Goal! - Wayne Routledge - Swansea 2 - 2 Reading Wayne Routledge finds the net with a goal from close range low into the middle of the goal. Swansea 2-2 Reading.
Corner taken by Sung-Yeung Ki, Headed effort from deep inside the area by Ashley Williams misses to the right of the goal.
Luke Moore takes a shot. Save by Alex McCarthy. Corner taken by Ben Davies from the right by-line.
Booking Jason Roberts goes into the referee's book.
Substitution Jason Roberts comes on in place of Noel Hunt.
The assist for the goal came from Wayne Routledge.
70:30 Goal scored
Goal! - Miguel Michu - Swansea 1 - 2 Reading Miguel Michu grabs a headed goal from inside the penalty box. Swansea 1-2 Reading.
Miguel Michu fouled by Jay Tabb, the ref awards a free kick. Pablo Hernandez restarts play with the free kick.
Unfair challenge on Leon Britton by Pavel Pogrebnyak results in a free kick. Direct free kick taken by Chico.
Effort from just outside the area by Sung-Yeung Ki goes over the bar.
Miguel Michu gives away a free kick for an unfair challenge on Jem Karacan. Direct free kick taken by Alex McCarthy.
Sung-Yeung Ki takes a shot. Alex McCarthy makes a save. Corner taken by Sung-Yeung Ki from the left by-line, clearance by Adrian Mariappa. Inswinging corner taken from the right by-line by Ben Davies, Ashley Williams takes a shot. Save by Alex McCarthy. Inswinging corner taken by Sung-Yeung Ki, Pavel Pogrebnyak manages to make a clearance.
Wayne Routledge gives away a free kick for an unfair challenge on Pavel Pogrebnyak. Free kick taken by Alex McCarthy.
Substitution Nathan Dyer goes off and Pablo Hernandez comes on.
Angel Rangel takes a shot. Blocked by Jobi McAnuff.
Direct free kick taken by Ben Davies.
Booking Jay Tabb booked.
Foul by Jay Tabb on Miguel Michu, free kick awarded.
Chico concedes a free kick for a foul on Noel Hunt. Free kick crossed by Nicky Shorey, Chico manages to make a clearance.
Sung-Yeung Ki takes the inswinging corner, Noel Hunt makes a clearance.
Noel Hunt fouled by Ashley Williams, the ref awards a free kick. Direct free kick taken by Shaun Cummings.
Luke Moore takes a shot. Blocked by Shaun Cummings. Luke Moore takes a shot. Alex McCarthy makes a save.
Free kick awarded for an unfair challenge on Ashley Williams by Pavel Pogrebnyak. Free kick taken by Michel Vorm.
Jay Tabb fouled by Wayne Routledge, the ref awards a free kick. Kaspars Gorkss takes the free kick.
Free kick awarded for a foul by Nicky Shorey on Nathan Dyer. Angel Rangel takes the direct free kick.
Jimmy Kebe is ruled offside. Michel Vorm takes the free kick.
Luke Moore takes a shot. Save by Alex McCarthy.
The game restarts for the second half.
Substitution Luke Moore replaces Danny Graham.
45:00 +2:28 Half time
Half Time The ref blows to end the first period.
Jobi McAnuff takes a shot. Angel Rangel gets a block in.
The assist for the goal came from Jobi McAnuff.
43:21 Goal scored
Goal! - Noel Hunt - Swansea 0 - 2 Reading Noel Hunt scores a goal from inside the six-yard box to the top left corner of the goal. Swansea 0-2 Reading.
Free kick taken by Alex McCarthy.
Booking Miguel Michu is cautioned by the ref for unsporting behaviour.
Miguel Michu concedes a free kick for a foul on Adrian Mariappa.
Noel Hunt challenges Ashley Williams unfairly and gives away a free kick. Michel Vorm takes the free kick.
The ball is delivered by Pavel Pogrebnyak, Jem Karacan takes a shot. Save made by Michel Vorm.
The assistant referee signals for offside against Miguel Michu. Free kick taken by Alex McCarthy.
Nicky Shorey takes a outswinging corner to the near post, Danny Graham manages to make a clearance.
Sung-Yeung Ki gives away a free kick for an unfair challenge on Jay Tabb. Nicky Shorey takes the free kick.
Free kick awarded for a foul by Noel Hunt on Leon Britton. Danny Graham takes the direct free kick.
Centre by Jimmy Kebe, clearance made by Angel Rangel.
Sung-Yeung Ki takes a shot. Save made by Alex McCarthy.
The assist for the goal came from Jobi McAnuff.
30:33 Goal scored
Goal! - Pavel Pogrebnyak - Swansea 0 - 1 Reading Pavel Pogrebnyak finds the back of the net with a goal from inside the area low into the middle of the goal. Swansea 0-1 Reading.
The referee blows for offside against Pavel Pogrebnyak. Direct free kick taken by Michel Vorm.
Wayne Routledge takes a shot. Blocked by Adrian Mariappa. Shot on goal by Miguel Michu from just inside the area goes over the target.
Foul by Noel Hunt on Danny Graham, free kick awarded. Michel Vorm takes the direct free kick.
Sung-Yeung Ki challenges Noel Hunt unfairly and gives away a free kick. Direct free kick taken by Nicky Shorey.
The referee blows for offside against Pavel Pogrebnyak. Free kick taken by Chico.
Inswinging corner taken left-footed by Ben Davies from the right by-line to the near post, Noel Hunt manages to make a clearance.
Corner from the left by-line taken by Sung-Yeung Ki, Close range header by Ashley Williams goes over the bar.
Centre by Noel Hunt.
Wayne Routledge takes a shot. Save by Alex McCarthy.
Free kick crossed right-footed by Sung-Yeung Ki.
Booking Adrian Mariappa goes into the referee's book.
Adrian Mariappa gives away a free kick for an unfair challenge on Miguel Michu.
The assistant referee flags for offside against Pavel Pogrebnyak. Indirect free kick taken by Leon Britton.
Wayne Routledge produces a cross, Danny Graham takes a shot. Save by Alex McCarthy. Corner taken by Sung-Yeung Ki, Headed effort from deep inside the penalty area by Ashley Williams misses to the right of the target.
The official flags Noel Hunt offside. Ashley Williams takes the indirect free kick.
The assistant referee signals for offside against Danny Graham. Nicky Shorey takes the free kick.
Nathan Dyer fouled by Jay Tabb, the ref awards a free kick. Sung-Yeung Ki crosses the ball, Header from close range by Ashley Williams misses to the right of the target.
Inswinging corner taken by Sung-Yeung Ki.
Foul by Noel Hunt on Sung-Yeung Ki, free kick awarded. Sung-Yeung Ki takes the free kick.
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