Heart of Midlothian 0 Celtic 2
The visitors always looked in command as the Hearts' faithful left bemoaning their side's lack of fight.
Despite a scrappy opening, the champions went ahead in only the seventh minute.
Janos Balogh seemed to get a good fist on an Andreas Hinkel free-kick only for the ball to land at the feet of Shaun Maloney 25 yards out.
Maloney looked up and hit an unstoppable first-time shot over Balogh and into the empty net.
Celtic grabbed their second in the 20th minute, with ex-Hibs man Gary Caldwell applying the final touch.
The goal came from a fine in-swinging corner by Paul Hartley which Barry Robson headed towards goal.
Balogh did well to keep out Scott McDonald's flick, but Caldwell was on hand to finish in the ensuing melee.
Celtic were by now controlling the game with Hearts' only effort on goal being an Andrew Driver free-kick which curled just wide on 25 minutes.
Caldwell nearly scored his second just before half time. He was picked out in the area by Hartley, but the centre-half could only deliver a defender's finish and skewed the ball wide.
Hearts' cause was further dented just six minutes in the second half when Marius Zaliukas was given his marching orders for holding back McDonald in the box.
Hartley could not inflict further damage as he fired the resulting penalty wide.
From then on, Hearts seemed to be sticking to damage limitation and made their intentions clear when bringing on Jamie Mole to replace their lone striker Christian Nade on the hour.
The home fans made their feelings clear at that change, but boos almost turned into cheers as Christophe Berra saw a header fly just wide minutes later.
Towards the end, Hearts did manage to get their first shots on target but Michael Stewart and Mole both found Artur Boruc's safe hands from distance as the match petered out.