Georgios Samaras fired his second winner this week to send Celtic back to the top of the Clydesdale Bank Premier League.
The Greek forward drilled home in the 34th minute following a Kris Commons through-ball and Celtic comfortably saw out the win even if their performance failed to match the spark of their maiden Champions League away win against Spartak Moscow.
Celtic, who were briefly knocked off top spot by Hibernian, were flat at the start of the second half before exerting some decent pressure in the final quarter.
Callum Paterson had missed a great chance to give Hearts the lead before Celtic lifted their game with Commons again at the heart of their best play.
The Bhoys were without Scott Brown, who continues to battle a hip problem, and lost his Scotland team-mate Charlie Mulgrew in the first half following an early collision with Hearts goalkeeper Jamie MacDonald, who was carried off with a bad head knock.
Another player in the Scotland squad for the World Cup double-header against Wales and Belgium, Andy Webster, was in the Hearts team after a back injury.
MacDonald was on the park long enough to force wide Mulgrew's shot after a brilliant first-time return pass from Commons.
But there were immediate signals he would be unable to continue after he bravely attacked Emilio Izaguirre's cross to punch the ball away from a crowd of players before Commons and James Forrest failed to convert the loose ball.
The goalkeeper was taken off wearing a neck brace to warm applause from around the stadium with Peter Enckelman taking his place in the 13th minute.
Mulgrew played on, although only temporarily.
Celtic, wearing their new 125th anniversary white change strip with black shorts, initially found it difficult to break down Hearts' solid formation and Paterson should have scored in the 25th minute after Andrew Driver slid in to dispossess Kelvin Wilson as the Celtic defender tried to shepherd the ball behind for a goal kick.
Driver laid the ball back but Paterson fired wide from 12 yards. The teenager was stretching but he should have done better with the goal gaping.
Celtic responded when Samaras met a Commons cross with a controlled first-time volley which hit the outside of the post.
Mulgrew left the field, apparently concussed, and handed the captain's armband to Samaras, who took just two minutes to embrace his new-found responsibility with the opener.
Commons was the provider with a pass with the outside of the foot into the left channel and the Greece striker ran on to it and fired a left-foot shot through the legs of Enckelman.
Commons almost caught the substitute goalkeeper out with a quick free-kick moments later but the ball sailed just wide.
Hearts were still posing a threat from long range - Driver saw a curled effort deflected wide with Fraser Forster wrong-footed, Ryan Stevenson fired an effort just wide and the Celtic goalkeeper tipped over Mehdi Taouil's powerful strike.
The champions came closer in the sixth minute of injury-time after some sharp build-up play from all their forward players that ended with Commons firing across the face of goal and just beyond the post with Gary Hooper just too far away to convert.
Hearts lost another player to injury in the 52nd minute when John Sutton replaced Paterson, who had taken a knock on the back of his leg.
The visitors were keeping Celtic in their own half without creating any chances and Neil Lennon made a change in the 70th minute, replacing Hooper with Beram Kayal and moving to a 4-3-3.
The tactical change immediately worked.
Commons fired just over the top corner after good skill in the box and Enckelman pushed Izaguirre's strike past his near post after the left-back had nutmegged Ryan McGowan.
Samaras headed over Commons' cross from six yards and Enckelman saved from Forrest as the winger stumbled on to a left-footed shot before palming away a Commons shot in unorthodox fashion.
Samaras had another good chance in injury-time but he failed to connect with substitute Miku's return ball from close range and Celtic survived a last-gasp scare when Driver fired an angled drive just wide.