Record signing Arne Engels and Luke McCowan scored their first Celtic goals to maintain their winning start after Hearts were controversially denied a penalty.
Belgian Engels, who completed his £11m move on deadline day, fired home from the spot in the second half after James Penrice was penalised for handball.
Hearts striker Lawrence Shankland saw his header come off Liam Scales' arm before the break only for VAR to overturn the penalty decision.
McCowan saw his ball go in off the post just eight minutes after he came off the bench, with Adam Idah's stoppage-time goal ruled out for offside.
It is the first time Celtic have won five league matches without conceding since 1907, while Hearts are bottom of the Premiership with one point.