Christopher Jullien was Celtic's match-winner but the big defender admits he was just relieved not to be the Hoops' fall guy after gifting Hamilton their opener.
The Frenchman let Marios Ogkmpoe get past him as the Greek frontman nodded Accies ahead at the Foys Stadium.
Odsonne Edouard soon levelled up with a free-kick after Jamie Hamilton's red card but it looked like an opportunity was set to be missed as the hosts defended for their lives.
But Celtic's siege paid off with 12 minutes remaining as Jullien steered home Ryan Christie's cross.
It was another big goal from the centre-back after his strikes against Europa League rivals Lazio and Rangers in the Betfred Cup final - and it opened the floodgates as Edouard and James Forrest added further strikes late on.
Celtic are now seven points clear of Rangers, who have a game in hand at the top but Jullien was just glad he was not to blame for any dropped points.
He said: "Scoring is not my first goal on the field. My first goal is a clean sheet. I was really mad about the goal we conceded because it was my player who scored. My goal is a bonus."
The Hoops have now put daylight between themselves and Rangers but Jullien is not getting carried away.
He said: "We don't talk about the finish to the league right now. It's a lot of months ahead. We are just focused on the next game. We are just happy about the result."