The Devils, who had lost their previous two games, moved two points in front of Pittsburgh for the lead in the Atlantic Division.
Martin Brodeur needed to make just 17 saves to get the victory, the 664th of his career. He has an 8-4 record this year with two of those losses coming in overtime.
New Jersey faced a 2-1 deficit heading into the final period, but Loktionov tied it 9:19 into the stanza with a slap shot that produced his first goal of the season.
Kovalchuk scored the game-winner on the power play with 8:20 to play.
Patrik Elias delivered the other New Jersey goal shorthanded midway through the second period that forged a 1-1 tie. Mike Ribeiro temporarily put Washington in front at 2-1 with 7:20 to go in the first.
Braden Holtby stopped 34-of-37 shots in taking the loss.