Anthony Stokes scored one goal and set up two more as Celtic showed sufficient class to overcome Hearts' youthful enthusiasm at Tynecastle.
Hearts strongly contested the 19th-minute penalty tucked away by Kris Commons after Stokes' header struck the hand of defender Jamie Hamill.
Jason Holt's low drive levelled the game 13 minutes after the break.
But Stokes fired Celtic back in front then teed up Teemu Pukki for a headed third on his debut from the bench.
It was the reigning champions' third straight domestic away win and stretched their unbeaten run to four games since losing the first leg of their Champions League qualifier against Shakhter Karagandy.
The three points took the second-placed Celtic level on points with Inverness Caledonian Thistle ahead of the Highlanders' visit to Kilmarnock.
And they were rewarded for Celtic manager Neil Lennon fielding a strong, unchanged side despite the proximity of Wednesday's Champions League group stage opener away to AC Milan.
There was also a continuation of the fine form shown by Scott Brown with Scotland as he dictated early play from midfield balanced heavily in favour of the visitors.
Celtic's flowing football was easy on the eye, but Hearts' defence, outclassed by leaders Inverness before the international break, had been bolstered by suspension-free Danny Wilson and Kevin McHattie and were preventing clear-cut chances.
Hearts looked lively on the break and, a free-kick having been won wide on the right, McHattie's whipped ball into the six-yard box was pushed nervously clear by goalkeeper Fraser Forster as it curled towards the far corner.
Dutch winger Derk Boerrigter was firing some dangerous crosses into the Hearts penalty box and one found Commons in space 12 yards out, but the volley powered well over the crossbar.
Home striker Callum Paterson was left bloodied by a forearm smash into his nose from Stokes that referee Collum ruled was accidental.
Hearts were seeing red again minutes later when Hamill conceded a controversial penalty for the second game running.
The experienced midfielder had his red card against Inverness overturned as television footage showed it had struck his head.
There was no question this time that Stokes' header deflected off Hamill's arm after a bit of penalty box wrestling, but Hearts will argue it is was certainly not a deliberate movement towards the ball and debatable whether the effort was a threat to the goal.
Commons wrong-footed Jamie MacDonald from the penalty spot and soon turned provider with a precise low pass behind the defence that was tucked away by Stokes, but the striker was marginally offside.
MacDonald did well to palm away a powerful 20-yard drive from Matthews, but the full-back again shining as a midfielder was to hobble off soon after.
The Welshman was the victim of a superb last-gasp tackle from Wilson and could be a worry for Celtic's trip to Italy.
Hearts had been shot shy on their rare sights at goal, but that changed after the break when McHattie's effort was deflected to Holt on the edge of the box and Scotland Under-21 midfielder low drive through a sea of legs evaded Forster's outstretched toe.
Home joy only lasted six minutes as Commons' header pierced the Hearts rearguard and Stokes sped clear to poke the ball past MacDonald.
There were muted shouts for a penalty by the home side, but they never looked like recording a third straight home win against a side that has now fired 11 goals past them in the last three meetings.
Celtic's icing on the cake came when Stokes' clever flick over goalkeeper MacDonald gave recent signing Pukki the chance to mark his arrival moments earlier with a simple finish.