Danny Graham scored his 100th career goal to secure victory for Swansea over Liverpool to end their debut Premier League season on a high.
Graham struck from close range with four minutes remaining to secure a memorable win.
Swansea had dominated the first half and Gylfi Sigurdsson twice went close to giving them the lead.
Liverpool were much improved after the break and Andy Carroll's overhead kick was saved by Michel Vorm.
There was a carnival atmosphere at the Liberty Stadium with many home fans dressed as Elvis to celebrate Swansea's first season in the Premier League.
Swansea fans dress as Elvis to celebrate their first season in the Premier League
Swansea enjoyed plenty of early possession and Joe Allen dispossessed Jonjo Shelvey but his shot across the face of goal eluded Graham at the far post.
Liverpool's nervy start continued as goalkeeper Alexander Doni, in for Pepe Reina, was penalised for picking up a long back pass from Andy Carroll.
From the resultant free-kick Gylfi Sigurdsson passed the ball short to Scott Sinclair but his shot was deflected over for a corner.
Liverpool's first chance of note came on 14 minutes when Maxi Rodriguez, in possibly his final game for the Reds, flashed a shot wide of the post.
But Swansea continued to control the game and Sigurdsson saw his shot blocked on the line by Maxi following Allen's corner.
The visitors were finding it hard to get a foothold in the game although Ashley Williams was forced to head clear Shelvey's effort from the edge of the area.
Sigurdsson, after being fouled by Shelvey, hit a free-kick low past the edge of the wall but Doni got down to his right to tip the ball round the post.
Match of the Day commentator
"It's another memorable victory for Swansea City in a season that will go down in the history of this club as one of their very best. Brendan Rodgers' team getting all three points on the final day of the season thanks to a late goal from Danny Graham."
Liverpool showed very little threat in front of goal with striker Andy Carroll directing a header straight at Vorm before firing a shot wide.
Dyer should have done better when Sigurdsson's pass put him in the open but he shot straight at Doni.
Carroll's frustration boiled over during the final minute of the first half when he was involved in a scuffle with Swans captain Ashley Williams and both players were booked by referee Mark Halsey.
Liverpool started the second half with more purpose with Jordan Henderson firing straight at Vorm.
Carroll came closest to opening Liverpool's account when he hit a spectacular overhead kick which forced Vorm into a fine save.
Substitute Craig Bellamy flashed a shot well wide of the post before Neil Taylor snuffed out an opportunity for his Wales team-mate, who was bearing down on goal.
Liverpool looked the more likely side to score as the game entered its final stages with Carroll's low shot forcing Vorm into another save.
But it was the home side who finally broke the deadlock with four minutes remaining
Watch Brendan Rodgers' last interview as Swansea manager
Angel Rangel and Sinclair combined on the right and Graham converted coolly from close range for his 14th goal of the season.
The victory meant Swansea finished their first season in the Premier League in 11th with Liverpool completing the campaign in eighth position.
Swansea manager Brendan Rodgers:
"It's been a wonderful day for the football club and all the credit to the players and the supporters.
"We started out on an incredible journey at the beginning of the season - it was the first Welsh club into the Premier League
"To finish it off with 14 clean sheets, playing how we wanted to play and to arrive in 11th place is an incredible achievement.
"It's important now to celebrate that success and look to improve over the summer and go again for next season."
Kenny Dalglish's last interview as Liverpool manager
Liverpool manager Kenny Dalglish:
"If there was going to be a goal I thought it was going to be us who scored it. There was never going to be much in it. Unfortunately for us they got it.
"Congratulations to Swansea, they've done fantastic.
"They've had a great season and to win in front of their home fans in the last game of the season will send them away through the summer with a good taste in their mouth."
Full Time The referee blows for the end of the match.
Inswinging corner taken from the left by-line by Craig Bellamy, Close range headed effort by Daniel Agger misses to the right of the goal.
Substitution Mark Gower replaces Gylfi Sigurdsson.
Assist by Angel Rangel.
85:52 Goal scored
Goal! - Danny Graham - Swansea 1 - 0 Liverpool Danny Graham finds the net with a goal from close in to the bottom right corner of the goal. Swansea 1-0 Liverpool.
Luis Suarez takes a shot. Blocked by Ashley Williams.
Scott Sinclair takes a shot. Blocked by Jamie Carragher.
Dirk Kuyt takes a shot. Blocked by Ashley Williams.
Substitution Nathan Dyer leaves the field to be replaced by Wayne Routledge.
Neil Taylor delivers the ball.
Unfair challenge on Gylfi Sigurdsson by Dirk Kuyt results in a free kick. Ashley Williams restarts play with the free kick.
Shot by Andy Carroll from 12 yards. Michel Vorm makes a save.
Luis Suarez takes the outswinging corner, Daniel Agger takes a shot. Michel Vorm makes a save.
Substitution Dirk Kuyt replaces Rodriguez Maxi.
Free kick awarded for an unfair challenge on Luis Suarez by Joe Allen. The free kick is swung in right-footed by Craig Bellamy.
Nathan Dyer is penalised for a handball. Direct free kick taken by Glen Johnson.
Craig Bellamy produces a right-footed shot from just outside the area that goes wide left of the goal.
Handball by Gylfi Sigurdsson. Free kick taken by Jordan Henderson.
Gylfi Sigurdsson takes the outswinging corner, Steven Caulker has a headed effort from close range and clears the bar.
Shot from inside the six-yard box by Angel Rangel goes wide right of the target.
Corner taken by Gylfi Sigurdsson, Andy Carroll manages to make a clearance.
Substitution (Liverpool) makes a substitution, with Craig Bellamy coming on for Stewart Downing.
Effort on goal by Scott Sinclair from inside the area goes harmlessly over the bar.
Neil Taylor challenges Andy Carroll unfairly and gives away a free kick. Stewart Downing takes the direct free kick.
Andy Carroll takes a shot. Michel Vorm makes a save.
Andy Carroll takes a shot. Steven Caulker gets a block in. Inswinging corner taken right-footed by Rodriguez Maxi, Corner taken by Stewart Downing from the right by-line to the near post, clearance by Gylfi Sigurdsson.
Free kick awarded for an unfair challenge on Daniel Agger by Gylfi Sigurdsson. Direct free kick taken by Alexander Doni.
Jordan Henderson takes a shot. Michel Vorm makes a save.
Stewart Downing decides to take the corner short.
Gylfi Sigurdsson takes a shot. Blocked by Rodriguez Maxi.
The game restarts for the second half.
45:00 +3:06 Half time
Half Time The match has reached half-time.
Direct free kick taken by Jamie Carragher.
45:00 +1:10 Booking
Booking Ashley Williams booked.
45:00 +1:10 Booking
Booking Andy Carroll goes into the book.
Ashley Williams challenges Andy Carroll unfairly and gives away a free kick.
Nathan Dyer takes a shot. Save by Alexander Doni.
Close range strike by Andy Carroll goes over the bar.
Nathan Dyer concedes a free kick for a foul on Rodriguez Maxi. Direct free kick taken by Glen Johnson.
Andy Carroll takes a shot. Save made by Michel Vorm.
Neil Taylor takes a shot. Save by Alexander Doni.
Andy Carroll has an effort at goal from outside the penalty box missing to the wide right of the goal.
Scott Sinclair fouled by Martin Kelly, the ref awards a free kick. Free kick taken by Joe Allen.
Inswinging corner taken right-footed by Gylfi Sigurdsson from the left by-line, save made by Alexander Doni. Shot from just outside the box by Leon Britton misses to the right of the goal.
Foul by Jonjo Shelvey on Gylfi Sigurdsson, free kick awarded. Direct effort from the free kick comes in from Gylfi Sigurdsson, save by Alexander Doni.
Foul by Jonjo Shelvey on Leon Britton, free kick awarded. Angel Rangel restarts play with the free kick.
Corner taken by Gylfi Sigurdsson, clearance by Andy Carroll.
Jonjo Shelvey takes a shot. Ashley Williams gets a block in.
Outswinging corner taken right-footed by Joe Allen played to the near post, Gylfi Sigurdsson takes a shot. Blocked by Jamie Carragher.
Danny Graham is caught offside. Alexander Doni restarts play with the free kick.
Free kick awarded for an unfair challenge on Danny Graham by Jamie Carragher. Neil Taylor takes the free kick.
Shot from just outside the box by Rodriguez Maxi misses to the left of the target.
Gylfi Sigurdsson takes the indirect free kick. Scott Sinclair takes a shot. Jamie Carragher gets a block in. Gylfi Sigurdsson decides to take the corner short.
Shot by Joe Allen from deep inside the penalty area misses to the right of the target.
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