The league leaders dominated throughout but lacked a cutting edge in the final third until Kris Commons and Stefan Johansen struck within seven minutes of each other to settle the issue, John Guidetti and Commons icing the cake in the final quarter.
It was a 10th consecutive domestic success for Ronny Deila’s side and sets them up nicely for a pivotal week, with Inter waiting at the San Siro on Thursday before they host their dogged domestic pursuers Aberdeen in Glasgow next Sunday.
Accies remain in the top six despite having not won in six games and goalkeeper Michael McGovern was quickly called into action, saved superbly from Nir Bitton, who had been picked out by Commons’ free-kick, and player-manager Martin Canning hooked the loose ball clear.
McGovern again had to demonstrate his prowess to deny James Forrest from close range after the marauding Efe Ambrose had carved out the opening.
Scott Brown had to be alert to snuff out a Hamilton counter attack which was being led by debutant Nigel Hasselbaink.
Mikey Devlin did well to deny Guidetti as he looked to engineer an opening and Bitton and Commons both threatened as the pressure continued to build on the visiting side.
Guidetti again forged an opening but his finish lacked the power to trouble McGovern before Johansen shot straight at the Accies ‘keeper.
Adam Matthews replaced Jason Denayer at the break while Hamilton’s Ziggy Gordon was taken ill having taken a knock to the head and Louis Longridge deputised for the second period.
The pattern of play continued as Celtic probed and pressed against the resolute Accies rearguard before the breakthrough finally arrived courtesy of Commons as a rampaging Virgil van Dijk picked out the midfielder (57) who fired home from six yards.
McGovern prevents Celtic extending their lead with a good save from Guidetti before Johansen’s shot was deflected onto the post off Hendrie.
But the wind was in the Celtic sails now and Van Dijk was again the unlikely architect as he saw his shot parried by McGovern and Johansen (64) knocked in the rebound.
The Accies resistance was fading fast and Guidetti took full advantage, providing an emphatic headed finish (78) after substitute Stuart Armstrong and Emilio Izaguirre had done the spadework.
Four minutes later Commons completed a highly satisfactory afternoon as he slotted in with his right foot as Celtic thoughts turned to their date in the San Siro on Thursday night.