Two goals in three minutes, including a Stephen McManus own goal, gave Hearts an early boost with Roman Bednar sealing the win midway through the second half.
Celtic should have taken the lead after just two minutes as McManus lashed a shot at the Hearts goal. But Craig Gordon made a magnificent diving save to keep the ball out of the net.
McManus did strike five minutes later, but unfortunately for him he found the back of his own net. Paul Hartley blasted a shot at the Celtic goal and McManus headed past Artur Boruc while trying to clear his lines.
Hartley did claim a goal, his 16th of the season, on nine minutes with a quickly taken free-kick which caught the Celtic defence on the hop.
Hartley blasted the ball into the top corner of the net and despite protests from the visitors the goal stood.
Midway through the half Rudi Skacel could have made it three, but his shot cannoned off the upright, while at the other end Roy Keane missed a sitter sending his shot straight into the arms of Gordon.
Celtic fought back from 2-0 down on their New Year's Day visit to Tynecastle, but they rarely looked like breaking back into the game.
The result was put beyond doubt on 63 minutes when Bednar put an expert finish on a Hartley cross to make it 3-0.