Celtic 3 Heart of Midlothian 0
Both sides had chances but, where Celtic were clinical in their finishing, Hearts were wasteful.
Two goals early in each half by Celtic's strikeforce of Jan Vennegoor of Hesselink and Scott McDonald put the home team well on the way to all three points.
Andreas Hinkel scored his first goal for Celtic to make it three when he lashed the ball home from close range near the end.
Celtic went on the attack from the start and, after McDonald was fouled on the edge of the area, Shunsuke Nakamura curled a superb free-kick over the wall but watched in agony as it came back from the post.
Hearts keeper Steve Banks saved well from another Nakamura shot before Celtic's early pressure paid off.
Aiden McGeady skipped past Robbie Neilson's challenge and his cross was swept home by Vennegoor of Hesselink.
Andrius Velicka and Andrew Driver then made dangerous breaks for the visitors but lacked composure at the vital moment.
Hearts came close to equalising when Andrius Ksanavicius' cross took a deflection which looped over Artur Boruc, but Stephen McManus was on the line to head clear.
Hearts were enjoying a good spell of pressure and when Boruc could only push out Driver's shot, Velicka seemed certain to score but only found the side-netting.
The visitors squandered a good chance early in the second half when Driver outpaced Hinkel only to shoot tamely at Boruc.
Hearts were made to pay as Celtic went two up as, from Nakamura's corner, McDonald was amazingly left unmarked six yards from goal and headed home high into the net.
Boruc still had time to have his usual argument with his defence when Velicka's shot was just wide after a poor clearance by the keeper.
McManus rightly was not willing to accept any blame for the keeper's error before Gary Caldwell stepped in as peacemaker.
Celtic ensured victory when McGeady's clever flick put Hinkel through and the wing-back shot home high into the net.
Georgios Samaras hit the woodwork from 20 yards as Celtic looked forward to the visit of Barcelona on Wednesday.