Adam Matthews' late equaliser prevented leaders Inverness Caledonian Thistle, so often a thorn in Celtic's side, recording another victory in Glasgow.
Caley Thistle, the last Scottish team to win at the home of the Scottish champions in November, went ahead through Aaron Doran's 25-yard drive.
Richie Foran forced in a second after 35 minutes, but Charlie Mulgrew poked in a reply before the break.
Matthews fired home, but Celtic's run of nine straight home wins ended.
It means Caley Thistle remain three points clear of Celtic, who had won their last 13 top-flight outings on their own patch since that defeat by Inverness, at the top of the Scottish Premiership.
A much-changed Celtic side had taken to the field looking to recover from the 2-0 Champions League play-off defeat by Shakhter Karagandy - the Glasgow side's first in seven games this season.
The absence of James Forrest, Kris Commons and Georgios Samaras was the result of injuries, while Joe Ledley, Steven Mouyokolo and Mikael Lustig also dropped out, possibly with a view to being rested ahead of next week's second leg.
One of the incoming half-dozen, Tony Watt, should have opened the scoring when he found himself one-on-one against Dean Brill, but the Scotland Under-21 striker's attempt to steer the ball into the corner was too close to the goalkeeper.
The home side were quickly made to rue that missed chance when Caley Thistle took the lead.
Doran picked up the ball 25 yards from goal and curled it beautifully past Celtic goalkeeper Fraser Forster.
Nine minutes later and Celtic manager Neil Lennon was handed another injury headache, with midfielder Beram Kayal being forced out of the action and Ledley's rest period on the bench was cut short.
Brill did well to turn a low Watt drive wide, while Efe Ambrose, who had been returned to the Celtic defence, powered a header just over the Inverness crossbar as Celtic started to ramp up the pressure in search of an equaliser.
However, it was the visitors who stretched their lead when Foran reacted first to Billy McKay's mis-hit overhead kick to force home Caley Thistle's second.
Just when it looked like another surprise victory for Caley Thistle at Celtic Park was on the cards, Mulgrew pounced on a cut-back from Emilio Izaguirre to toe-poke past Brill.
Celtic failed to produce an equaliser before the half-time whistle relieved the rising pressure on the Caley Thistle defence.
Amido Balde, handed his first competitive start for Celtic, flicked a header just over the crossbar from a Watt cross as the summer signing came close to his first goal since arriving from Vitória Guimarães.
Inverness were now rarely seen in attacking mode but had claims for a penalty waved away as Doran, who had delayed his pass to an unmarked Nick Ross, was challenged by Virgil Van Dijk.
Celtic eventually got the equaliser their probing merited when a fine through ball from captain Scott Brown gave Matthews, making a rare start following injury problems, the chance to fire past Brill.
Substitute Mikael Lustig sent a late header just wide and Inverness held on for a point.
Live Text Commentary
Full Time The referee signals the end of the game.90:00 +3:24
Corner taken by Charlie Mulgrew from the right by-line.90:00 +2:59
Strike comes in from Charlie Mulgrew from the free kick.90:00 +2:13
Free kick awarded for a foul by Josh Meekings on Amido Balde.89:55
Shot by Efe Ambrose went over the crossbar.88:58
Torbjorn Agdestein takes a shot and goes harmlessly over the bar.87:01
Header by Mikael Lustig misses left.83:07 Substitution
Substitution Torbjorn Agdestein on for Billy McKay.82:15 Substitution
Substitution Marley Watkins is brought on as a substitute for Aaron Doran.81:57
The assist for the goal came from Scott Brown.81:57 Goal scored
Goal! - Adam Matthews - Celtic 2 - 2 Inverness Adam Matthews scores a right footed goal. Celtic 2-2 Inverness CT.80:28
Shot by Amido Balde. Dean Brill catches the ball.80:00 Substitution
Substitution Bahrudin Atajic joins the action as a substitute, replacing Tom Rogic.78:12
Headed chance falls to Amido Balde. Dean Brill catches the ball.77:55
Corner taken by Charlie Mulgrew.77:28
Clearance by Gary Warren.77:24
Charlie Mulgrew crosses the ball in from the free kick.76:49
Graeme Shinnie challenges Adam Matthews unfairly and gives away a free kick.75:25 Substitution
Substitution Mikael Lustig comes on in place of Virgil van Dijk.75:09
Joe Ledley takes a shot and went wide right of the net.
Nick Ross makes a clearance.74:40
The ball is crossed by Emilio Izaguirre.73:51
Clearance made by Joe Ledley.73:40
Free kick taken by Graeme Shinnie.73:22
Charlie Mulgrew concedes a free kick for a foul on Richie Foran.72:15
Gary Warren makes a clearance.72:13
The ball is sent over by Tony Watt.71:38
Gary Warren takes a shot and cleared the net.71:15
Corner from the right by-line taken by Graeme Shinnie.70:51
The ball is delivered by David Raven.70:18
Josh Meekings restarts play with the free kick.70:10
Free kick awarded for a foul by Tom Rogic on Richie Foran.69:28
Efe Ambrose takes a shot and goes over the bar.69:00
Clearance by Gary Warren.68:55
Emilio Izaguirre delivers the ball.68:42
Clearance by Ross Draper.68:39
A cross is delivered by Tony Watt.67:23
Charlie Mulgrew restarts play with the free kick.67:18
Unfair challenge on Charlie Mulgrew by Nick Ross results in a free kick.65:34
Corner from the left by-line taken by Adam Matthews.65:13
The ball is delivered by Tony Watt.63:50
Clearance by Richie Foran.63:21
Free kick crossed by Charlie Mulgrew.63:14
Tony Watt fouled by Gary Warren, the ref awards a free kick.62:32 Booking
David Raven receives a yellow card for time wasting.60:29
Free kick taken by Dean Brill.59:57 Booking
Amido Balde is booked.58:14
Header by Amido Balde goes harmlessly over the bar.56:39
Scott Brown restarts play with the free kick.56:35
Unfair challenge on Tom Rogic by Ross Draper results in a free kick.55:48
Header at goal by Amido Balde goes over the bar.55:32
Corner taken by Charlie Mulgrew.55:06
Emilio Izaguirre takes the free kick.55:02
The referee penalises Aaron Doran for handball.54:06
Free kick crossed by Graeme Shinnie.54:01
Free kick awarded for an unfair challenge on Nick Ross by Scott Brown.51:30
Aaron Doran takes a shot. Fraser Forster safely holds on.50:03
Header by Scott Brown goes over the bar.49:58
The ball is crossed by Emilio Izaguirre.48:26
Free kick taken by Josh Meekings.48:13
Foul by Virgil van Dijk on Billy McKay, free kick awarded.47:54
David Raven makes a clearance.47:50
Adam Matthews crosses the ball.47:18
Gary Warren makes a clearance.45:01
The referee starts the second half.45:00 +1:03 Half time
Half Time The ref blows to signal half-time.45:00 +0:44
Dean Brill manages to make a clearance.45:00 +0:40
Corner taken by Adam Matthews from the left by-line.45:00 +0:26
Clearance by Josh Meekings.45:00 +0:17
Corner taken by Adam Matthews.44:54
The ball is swung over by Charlie Mulgrew.44:42
Corner from the right by-line taken by Charlie Mulgrew.44:16
Adam Matthews sends in a cross.43:37
Gary Warren makes a clearance.43:34
The ball is delivered by Tony Watt.42:57
Header by Joe Ledley misses to the right of the target.42:46
Tony Watt crosses the ball.42:29
Clearance made by Graeme Shinnie.42:23
Emilio Izaguirre produces a cross.41:17
Assist by Emilio Izaguirre.41:17 Goal scored
Goal! - Charlie Mulgrew - Celtic 1 - 2 Inverness Charlie Mulgrew scores a left footed goal. Celtic 1-2 Inverness CT.34:58 Goal scored
Goal! - Richie Foran - Celtic 0 - 2 Inverness Richie Foran scores with a header. Celtic 0-2 Inverness CT.34:58
Billy McKay has an effort at goal and missed to the right of the net.34:58
The assist for the goal came from Billy McKay.33:39
Clearance made by Virgil van Dijk.33:33
Josh Meekings takes the free kick.33:03
Tom Rogic concedes a free kick for a foul on Ross Draper.32:12
Header at goal by Virgil van Dijk to the left of the net.31:58
Corner taken by Charlie Mulgrew from the left by-line.31:13
Clearance made by Graeme Shinnie.31:08
Centre by Emilio Izaguirre.29:50
The ball is delivered by Emilio Izaguirre.29:05
Header at goal by Efe Ambrose goes over the bar.28:47
Charlie Mulgrew restarts play with the free kick.28:18
Scott Brown fouled by Richie Foran, the ref awards a free kick.26:56
Dean Brill takes the free kick.26:43
Free kick awarded for a foul by Tom Rogic on Josh Meekings.26:25
Gary Warren makes a clearance.26:20
Emilio Izaguirre produces a cross.26:12
Josh Meekings manages to make a clearance.26:07
Scott Brown produces a cross.24:50
Centre by Emilio Izaguirre.23:23
Clearance made by Josh Meekings.23:15
Corner taken by Charlie Mulgrew from the right by-line.23:02 Substitution
Substitution Joe Ledley replaces Beram Kayal.22:41
Shot by Tony Watt. Dean Brill parries the ball away.20:33
Adam Matthews produces a cross.17:12
Shot by Tom Rogic missed to the left of the target.16:20
Virgil van Dijk takes the free kick.16:11
The offside flag is raised against Billy McKay.14:34
Shot from the free kick by Charlie Mulgrew went wide of the left-hand post.14:00
Free kick awarded for an unfair challenge on Tony Watt by David Raven.13:21
Assist on the goal came from Nick Ross.13:21 Goal scored
Goal! - Aaron Doran - Celtic 0 - 1 Inverness Aaron Doran grabs a goal with a right foot finish. Celtic 0-1 Inverness CT.12:37
Tony Watt takes a shot. Dean Brill safely holds on.12:23
Corner taken by Richie Foran from the right by-line.12:03
Graeme Shinnie sends in a cross.11:54
Corner from the right by-line taken by Graeme Shinnie.10:55
Headed chance falls to Amido Balde. Dean Brill catches the ball.9:30
Tom Rogic takes a shot.8:24
Aaron Doran takes a shot and went wide of the left-hand post.8:14
Free kick taken by Aaron Doran.7:27
Billy McKay fouled by Virgil van Dijk, the ref awards a free kick.7:12
Josh Meekings takes the free kick.6:54
Free kick awarded for a foul by Beram Kayal on Aaron Doran.4:16
Corner taken by Charlie Mulgrew from the right by-line.2:54
Dean Brill takes the free kick.2:45
Efe Ambrose gives away a free kick for an unfair challenge on James Vincent.2:33
Corner from the right by-line taken by Charlie Mulgrew.2:02
The ball is crossed by Adam Matthews.1:08
Beram Kayal restarts play with the free kick.1:04
Foul by Ross Draper on Tom Rogic, free kick awarded.0:00
The game kicks-off.
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