By Clive Lindsay
Massimo Donati scored a superb solo goal at Celtic Park
Shunsuke Nakamura's wayward volley struck Christophe Berra's arm and bounced into the Hearts net.
Massimo Donati slipped past two challenges before sliding home the second after 18 minutes.
Scott Brown forced home a third after the break, Jan Vennegoor of Hesselink added the fourth from the penalty spot and Nakamura curled in the fifth.
Celtic were unchanged following last weekend's victory over Aberdeen, with in-form striker Kenny Miller having aggravated his hamstring injury playing for Scotland.
Hearts made four changes, with Lee Wallace, Eggert Jonsson, Ruben Palazuelos and Andrius Velicka dropping out the squad completely following their draw with Gretna.
In came striker Calum Elliot, defender Jose Goncalves and midfielders Saulius Mikoliunas and Laryea Kingston.
Hearts started positively, despite playing Elliot as their lone striker, but looked surprisingly fragile in defence.
And, when Scott McDonald crossed to the back post, Nakamura's drive from 16 yards deflected off Berra's arm and bounced into the corner of the net.
Donati made it two after 22 minutes following a jinking run that left Kestutis Ivaskevicius and Berra floundering on their backs before the Italian drove low into the far corner from just inside the box.
Shunsuke Nakamura (centre) helped Celtic open the scoring
Hearts came close to pulling a goal back following a surging run by Kingston.
The Ghanaian's drive from 20 yards struck the post and rebounded back into his path, but Stephen McManus managed to deflect the follow-up effort over the crossbar.
McDonald forced two good goalline blocks from goalkeeper Steve Banks after the Australian striker got clear of his marker around the six-yard box.
Kingston had to clear off his own goalline after Vennegoor of Hesselink rose to meet a corner.
Boruc did well to save at the feet of Ivaskevicius after the Lithuanian raced into the Celtic penalty box.
But that burst of life did not satisfy the Hearts management team, with the Lithuanian being withdrawn with two others at half-time.
Kingston was a surprise departure along with Goncalves, with Andrew Driver, Neil McCann and Karapidis coming on as Hearts went for broke.
Driver ought to have pulled a goal back after dispossessing Mark Wilson but fired wide from the edge of the box.
The Edinburgh side paid for that miss when Brown fired home from five yards after 61 minutes.
And, two minutes later, Berra pulled down Nakamura after being nutmegged by the Japan midfielder,with Vennegoor of Hesselink sweeping in the resulting penalty kick.
Scott Brown powered forward before slipping the ball to Nakamura to add the fifth from 10 yards after 79 minutes.
Hearts' day became worse still when McCann was stretchered off for a late challenge on McDonald.
Celtic: Boruc, Wilson, Caldwell, McManus, Naylor, Nakamura, Scott Brown, Donati, McGeady (Riordan 69), Vennegoor of Hesselink (Killen 69), McDonald (Zurawski 87).
Subs Not Used: Mark Brown, Hartley, Sno, O'Dea.
Goals: Berra 9 og, Donati 22, Scott Brown 61, Vennegoor of Hesselink 63 pen, Nakamura 79.
Hearts: Banks, Neilson, Zaliukas, Berra, Goncalves (Karipidis 46), Mikoliunas, Stewart, Kingston (McCann 46), Ksanavicius, Ivaskevicius (Driver 46), Elliot.
Subs Not Used: Kurskis, Pospisil, Cesnauskis, Divine.
Booked: Ivaskevicius, Berra.
Att: 57,300
Ref: I Brines
Celtic challenged ' lead at the top of the SPL with a 5-0 thumping of  in reply to Rangers' 7-2 thrashing of Falkirk last Saturday.

After ten minutes, Shunsuke Nakamura's off-target volley hit Christophe Berra's arm and flew into the Hearts net. 15 minutes later,  Massimo Donati took on two Hearts defenders before sliding home the second. Scott Brown hit home a third 65 minutes in, 1 minute later, Jan Vennegoor of Hesselink scored the fourth from the penalty spot and Nakamura curled in the fifth on the 79 minute mark. Chris Killen had a good shot saved by the dispirited Hearts goalkeeper, Steve Banks.
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