A first-half strike was enough to claim Celtic's 10th consecutive victory and condemn Hamilton to their first defeat in six games.
A first-half strike from Leigh Griffiths was enough to claim Celtic's 10th consecutive victory and condemn Hamilton to their first defeat in six games.
The Hoops now hold an 11-point advantage over Rangers, having played two games less than their fierce Glasgow rivals.
Aberdeen missed the chance to narrow the gap to second-place Rangers when their game against Motherwell at Pittodrie was abandoned due to floodlight failure.
Despite the victory, Celtic manager Brendan Rodgers thought his side had not been at their usual standard.
"I think throughout most of this season we've performed at a really high level, but some games we haven't," the former Liverpool manager said.
"Tonight was one of those games that we didn't quite hit those heights, but we showed a great desire and persistence to keep going and we got the job done in the end."
Hamilton manager Martin Canning thought his side had been excellent.
"I thought their work-rate was different class and they did what they were asked to do," he said.
"It is a difficult place to come and it would've been nice to get something from it. But to come here and perform that way, I think the boys deserve some credit."
Celtic had gone into the first of three consecutive home games on the back of three comfortable away wins where they had racked up nine goals.
Hamilton were well aware of the threat the Glasgow giants could pose, having been thrashed 8-1 on their last visit to Celtic Park in January.
However, the visitors have shown themselves hard to beat this season following five consecutive draws, and proved disciplined in defence in the early stages.
Griffiths had grabbed a hat-trick on Hamilton's last visit on his way to clocking up 40 goals last season, only to find his opportunities more limited this season under Rodgers.
But a goal in his last run-out against Partick Thistle saw him keep his place in the starting line-up as he partnered the in-form Moussa Demble up front.
It was only the second time the pair had featured together from the start and the gamble paid off as they combined for the only goal in the 36th minute.
Australian international Tom Rogic threaded a through ball for Dembele to chase and the French forward squared to Griffiths, who held off the challenge of Grant Gillespie to fire into the empty net.
The Scotland international nearly had a second before the break as he raced onto a ball in the box, only to arrow a shot narrowly wide from a tight angle.
The chances began to come for Celtic at the start of the second half, with Griffiths blasting over from a Roberts cut-back before Dembele was off-target with a header as he blocked an attempted clearance.
Stuart Armstrong then scuffed a shot wide after racing into the box to collect a pass as the Hoops continued to be frustrated in front of goal.
Substitute Eamonn Brophy squandered a late chance for Hamilton when he fired wide after electing to shoot when team-mate Ali Crawford appeared to be in a better position.