Fasching cut it to 3-1 on a rebound at 14:52 of the third period, but Tom Wilson made it 4-1 when scored into an empty net at 15:44.
Cizikas cut it to 4-2, converting a pass from Bo Horvat during 6-on-5 situation, but Strome scored an empty-net goal at 18:50 for the 5-2 final.
It was Strome's 23rd goal, an NHL career high. He had 22 for the Chicago Blackhawks last season.
"It was good to get a win," Capitals coach Peter Laviolette said. "When you're losing games, it's deflating. It was good to get a good start, come out the right way, score goals right away -- a couple of goals right off the bat. … I thought [Kuemper] was really good. They fired a lot of shots tonight."
NOTES:Washington scored two or fewer goals in each of its previous five games. … Strome and Sandin combined for the fifth-fastest two goals to start a game in Capitals history. Gaetan Duchesne and Mark Taylor were the fastest (29 seconds on Oct. 27, 1985). … Wilson had two points (one goal, one assist), five hits and was plus-3 in 19:31 of ice time. … Washington captain Alex Ovechkin missed his second game because of an upper body injury. The Capitals won for the first time this season when he didn't play (1-7-0). … Washington blocked 27 shots, four each by Sandin and Fehervary. … Parise and Islanders defensemen Adam Pelech and Ryan Pulock were each minus-3. … Horvat has five points (one goal, four assists) in his past three games.