Couturier got the winner at 8:28 of the third period by tipping in a shot.
Philadelphia finished 3 for 3 on the power play.
CANADIENS 4, DEVILS 3, SO
NEWARK, N.J. (AP) — David Desharnais scored the tying goal with 37 seconds left in the third period and added a goal in the shootout and Montreal rallied for a victory over New Jersey.
Lars Eller also scored in third period and shootout for Montreal, which also beat the Devils in Montreal on Monday night.
Rookie Reid Boucher, making his NHL debut, scored for the Devils in the shootout, breaking a string of 20 straight missed chances by the Devils, who are 0-5 in shootouts this season.
The teams combined for five goals in the third period.
The Devils led 2-1 before Eller scored on a backhand to tie the score at 2-2 at 16:10.
Gionta scored in the first period to give Montreal a 1-0 lead and goalie Peter Budaj made it hold until Loktionov scored 4:19 into the third period to tie it at 1-1.