In front of a record crowd at the stadium of 6,007, Ronny Deila's side bossed the first-half with right-back Adam Matthews giving them the interval advantage in the 33rd minute with a terrific strike from 16 yards.
The visitors, back from a winter break in Gran Canaria, played with an assurance for the most part and, when midfielder Liam Henderson made it 2-0 five minutes into the second half with a drive, the points were effectively safe.
The champions move to within a point of the Dons albeit the Granite City men have the chance to re-establish their lead against Dundee later in the day, after which the champions will have two games in hand again.
Accies' 1-0 win at Celtic Park in early October had been their first victory over the Hoops in 76 years but there was little danger of lightning striking twice.
In their last outing, the visitors had performed impressively on the artificial pitch at Kilmarnock in their 2-0 win and they looked equally comfortable on a similar surface at Hamilton, which had been cleared of snow.
Led by skipper Scott Brown, wearing a bandage on his head to protect a cut, and with defender Jason Denayer and striker Leigh Griffiths in for Efe Ambrose and Stefan Scepovic respectively, the Parkhead side took early control.
Midfielder Kris Commons, as he had done against Killie, mounted a personal attack on the opposition goal, albeit failing to really trouble Accies keeper and captain, Michael McGovern.
In the 17th minute a Virgil van Dijk header from a Commons corner was easily saved by the Northern Irishman, although it seemed certain that there would be many more attempts to follow.
Hamilton player-interim coach Martin Canning, after leaving himself out for the home defeat to Dundee United on Monday night days after taking over from the departed Alex Neil, came back into the Accies' defence but they were showing little going forward.
However, the home side's first corner in the 26th minute caused panic in the visiting defence.
Ali Crawford's cross was cleared only to Accies' midfielder Tony Andreu, whose shot from the edge of the box was deflected up into the air with Denayer almost putting though his own goal, his wayward header saved by Craig Gordon with the Hoops keeper then blocking a close-range effort from Mickael Antoine-Curier.
However, any encouragement Accies took from that close call dissipated when the visitors took the lead, Matthews running on to a pass from Commons and firing first time high past McGovern from just inside the box with his first Celtic goal since August 2013.
There were only five minutes gone of the second half when Celtic doubled their lead.
A deep cross from Matthews from the right found Emilio Izaguirre and, when the ball fell to Henderson just inside the box, he drilled his shot low past McGovern and into the corner, with his first goal since March.
Accies, sensing the game was all but gone, went for broke.
Gordon was forced into a fine save down at his left-hand post by Dougie Imrie, moments before the Hamilton forward headed over the bar from six yards out.
However, Celtic remained steady, repelling anything Hamilton had to offer and indeed, in the 76th minute, McGovern was forced into fine save from a vicious Griffiths' drive as the Glasgow side flexed their muscles again.
Source : PA
Source: PA