Matt O'Riley's stoppage-time strike earned Celtic a dramatic 2-1 victory against a stubborn Motherwell side at Fir Park.
The midfielder, who agreed a new deal ahead of kick-off, fired in the winner in the 97th minute as Motherwell looked set to snatch a draw.
Luis Palma's cross crept in at the far corner to put Celtic ahead in the 88th minute but the Fir Park side, who had impressed, were soon level as Blair Spittal fired low into the net.
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Motherwell had a goal disallowed at 0-0 for Bevis Mugabi's foul on Hoops keeper Scott Bain.
The result maintains Celtic's unbeaten league start while Motherwell have suffered three straight defeats.
Chaos at Fir Park as Celtic snatch victory
The game had been on a knife edge throughout and Scott Bain, deputising for the suspended Joe Hart, made two good saves while the game was goalless.
O'Riley's new four-year deal was announced on the morning of the game and he showed his worth by converting a cushioned volley at the back post following Greg Taylor's cross.
The victory set Celtic up for the visit of Lazio in the Champions League on Wednesday and delivered another blow to Motherwell, who have now suffered narrow defeats against the top three in successive weeks.
Celtic had the bulk of the early possession but the only chances in the first quarter came from set-pieces. Spittal came close with an overhead kick and Liam Scales headed wide at the other end.
Motherwell were looking solid and Kyogo Furuhashi curled wide from 22 yards when Celtic did manage to pass the ball through the lines.
The home side had the best chance of the first half when Spittal's quick free-kick found Harry Paton's run. Bain came out to block Paton's shot with his foot and Celtic cleared the midfielder's driven cross on the rebound.
Liam Kelly made his only save of the opening 45 minutes from O'Riley after quick feet from Yang Hyun-jun before Spittal got Motherwell in behind again. However, Brodie Spencer could not find a final ball to capitalise.
James Forrest replaced Yang at half-time and Celtic began to show more urgency in the final third, although Taylor and Gustaf Lagerbielke could not make the most of half-chances.
Motherwell raised their own tempo in possession and had the ball in the net after Bevis Mugabi challenged Bain at a high ball. Stephen O'Donnell hit the ball off Mugabi on the line before knocking home the rebound and the offside flag went up. Mugabi's challenge might have been penalised anyway if the wing-back had netted first time.
Taylor created Celtic's best chance so far when he won the ball on the edge of the box and set up Daizen Maeda, but the Japanese attacker shot over with only Kelly to beat.
Motherwell responded and Theo Bair volleyed straight at Bain before the goalkeeper's feet again came to Celtic's rescue when he blocked Spittal's effort following Callum Slattery's through ball.
The home side looked tired as the game entered the final 10 minutes and Kelly saved Forrest's header after Palma's cross.
Then came the drama. Palma curled just inside the far post from outside the corner of the box as the ball whipped in between defender Dan Casey and Kelly. Fans spilled onto the track from behind the goal in the Tommy McLean Stand in showing their delight, but there was much more to come.
Motherwell found some energy and with plenty of players in the box, Spittal slotted into the far corner. Dozens of Motherwell fans were suddenly on the pitch themselves and they were barely back in their seats when O'Riley struck and sparked an even bigger pitch invasion.
Rodgers: We always fight until the end
Celtic manager Brendan Rodgers spoke to Sky Sports at full time:
"This club's history is built on fighting right until the end and we've scored so many late goals. We won 4-3 here before and that was right up there with that.
"A fantastic win for us and I'm delighted for the players.
"They had that ability to keep going and you're going to have to do that, especially against teams who sit in deep and tight. Stuart's team was very well organised and made things difficult for us.
"You have to find a way and the players did that today."
Kettlewell: The sorest defeat I've had
Motherwell manager Stuart Kettlewell admitted it was a hard one to take:
"It's probably as sore a defeat as I have had," he said.
"We have had a real tough run of games, going to Ibrox and playing against a high-flying St Mirren and then Celtic. But all I can comment on is how my players are acquitting themselves and I hope you see how well they have played
again.
"I accept at times Celtic dominate the ball and carve out probably more chances than there have been in the last two games we have had, but nobody can deny there was a real identity to our team again.
"We created some real good chances ourselves and showed that character to get back in the game. It's a bitter pill to swallow yet again."
What's next?
Motherwell's next Scottish Premiership match is away to Livingston on Saturday, October 7 while Celtic host Kilmarnock on the same day.
Both games kick-off at 3pm.