On the same power play, Wilson cut it to 2-1 at 15:57 when he redirected Erik Gustafsson's slap shot in the slot.
"I think the guys came together today and worked hard, but it's not easy to win in this league," Wilson said. "We've got to find a way here, and there's a good chunk of games left but … we've got to turn this around right now, start putting together some wins."
Suter pushed it to 3-1 at 6:24 of the third period, scoring blocker side from the slot after Evgeny Kuznetsov whiffed on a clearing attempt.
Suter has scored in three straight and has five goals in his past five games.
"Puck was bouncing around a little bit, and I think a great screen by [Oskar Sundqvist], and I just had to pick a corner," Suter said.
NOTES: Red Wings forward Jakub Vrana had two shots and was plus-1 in 11:31 of ice time in his first game since Oct. 15. Vrana, who was recalled from Grand Rapids of the American Hockey League on Feb. 14, was reinstated from the NHL/NHLPA Player Assistance program on Dec. 16. … Red Wings forward Robby Fabbri went to the locker room after blocking a shot late in the third period. There was no update. … Washington had not lost five straight in regulation since Jan. 15-24, 2014. … Capitals forward Anthony Mantha left the game in the second period with an upper-body injury. There was no update.