Belgian Engels, who sealed his £11m transfer on deadline day, confidently struck the ball into the back of the net from the penalty spot in the second half. The referee awarded the penalty after James Penrice was judged to have handled the ball in the box.
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.
TrendingEngels was chosen ahead of Paulo Bernardo after making his debut off the bench against Rangers two days after joining from Augsburg.
The midfielder twice came close in the first half, arriving in the box at the right time to fire wide in the third minute and hitting the inside of a post after a good flick by Kuhn.
Kyogo Furuhashi missed a great chance with Gordon rooted to the spot moments after being clattered by the Japanese striker.
Referee Colin Steven pointed to the spot in the first half when Shankland's header struck the arm of Scales from close range, but he reversed his decision after studying footage.
That decision looked to spur Hearts on and Shankland forced saves from Kasper Schmeichel from long range either side of the interval.
Steven Naismith's side survived a double scare just before the break when Gordon denied Furuhashi and Penrice made an excellent sliding block to deny Kuhn.
But the left-back was penalised for his next intervention and captain Callum McGregor persuaded Reo Hatate to hand the ball to Engels to send Gordon the wrong way from the spot.
Celtic struggled to build on the opener and Hearts came close when Blair Spittal's cross set up fellow sub Musa Drammeh. Schmeichel got down well to save.
McCowan settled the home fans' nerves with his first goal since joining from Dundee and Adam Idah was denied a goal in stoppage-time after VAR picked up an offside after he swept home Greg Taylor's low cross.