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.
Celtic will still win the title after going 19 points clear of Motherwell but manager Neil Lennon will be unhappy with the dropping of two points in a game that should have been over by the interval.
