Celtic had the first chance after eight minutes when Hooper was slipped through, but Darren Randolph made a great save to deny the striker.
Two minutes later, Scott Brown's shot was saved by Randolph. Victor Wanyama pounced onto the rebound, but he couldn't get his shot on target.
Kris Commons fired a shot just over as the Bhoys continued to put the pressure on the home side.
Commons was involved again on 14 minutes when he was brought down as he beared down on goal. The midfielder hit the resulting free kick against the wall.
Celtic finally made the breakthrough on 32 minutes. Commons passed to Hooper, who showed great control before finishing emphatically.
Two minutes later, Celtic made it 2-0. Brown got in behind Motherwell's defence and saw his cutback put into the net by Motherwell's Cummins.