Recently signed from Cardiff, Sainte-Luce was on hand with 10 minutes to go as he rifled home low from 25 yards to grab a priceless 1-0 victory.
The Dons enjoyed the better of a goalless first half as Jack Midson screwed an early shot wide.
Just beyond the half-hour Gary Alexander was denied by a super point-blank save from Daggers' keeper Chris Lewington.
The hosts replied with Abu Agogo seeing a 25-yard drive well saved by veteran stopper Neil Sullivan.
Minutes after the restart Dagenham came agonisingly close to an opener when Matt Saunders fired in a cracking shot from the edge of the box which whistled inches past the angle of post and crossbar.
They kept the pressure on and Luke Howell should have done better when he fired over the top.
The Dons worked their way back into the contest and Luke Moore slid a shot narrowly wide after latching on to Midson's flick.