During a New Jersey power play, Drouin-Deslauriers stopped Dainius Zubrus twice and Johnny Oduya to preserve a 1-0 advantage.
Drouin-Deslauriers came on in relief in Edmonton's last game, a 5-4 loss at Pittsburgh on Thursday night.
Sheldon Souray opened the scoring with 12:41 left in the second when he rifled a wrist shot through Devils goalie Scott Clemmensen's legs.
Just 6:30 later, Hemsky skated past two defenders before an attempt to poke the puck away by New Jersey's Jay Leach deflected off Hemsky's left skate and into the net for a power-play goal.
Zach Parise redirected Travis Zajac's shot with 16:10 left in the third period for the Devils' lone goal. Parise has 11 goals this season.
Clemmensen made 26 saves in his first NHL start since Jan. 3.
New Jersey is 1-3 since All-Star goalie Martin Brodeur went down with a torn left biceps on Nov. 1.
