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 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.
"It was a tough moment and a tough game. For sure that goal developed the situation. It was really welcome for the team and I'm really happy about the end."
The Hoops have now put daylight between themselves and Rangers – who still have a game in hand – 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.
"The title is a long marathon, it's a long race and each game is so important. It's three points. It's enjoyable to win for the team.
"It's the character we've had since the start of the year. We are confident about the way we play. We want to play our game, press high and get back the ball until we find the solution. So we are going to stick to our principles till the end because they are our strengths.
"I don't think about the other opponent in a game. Since the start of the year we have been really good. We showed our strength. After all the stuff about opponents we will see the count at the end."