In the 37th minute of a first-half controlled by the champions, defender Efe Ambrose scored his second goal in two games after costing the Hoops twice in their 3-0 Champions League last-16 defeat against Juventus a week ago.
The Perth side, who had deprived Celtic of five points in their previous two meetings this season, made a better fist of the second-half and had the ball in the net twice, only to see both efforts ruled out for offside but with eight minutes remaining Hasselbaink, on for Rowan Vine, curled a fantastic shot past Fraser Forster to stun the Parkhead side.
Dundee United spoiled James McFadden's Motherwell return as they recorded an impressive 1-0 win in the SPL at Fir Park.
Johnny Russell netted the only goal of the game after 17 minutes and despite piling on the pressure during the second-half the hosts were unable to come up with a response.
McFadden - who will be with the club for the rest of the season - made a late appearance from the bench, however he could not prevent Motherwell falling to their first home defeat of 2013.