Alex Ovechkin scored his 909th NHL goal and had an assist, and Logan Thompson made 30 saves for the Capitals (15-9-2), who have won seven of their past eight games.
Bo Horvat scored the lone goal for the Islanders (13-10-3), who are 1-3-1 through the first five of their seven-game homestand. Ilya Sorokin made 14 saves.
Thompson stacked the pads to deny Anders Lee’s snap shot off a 2-on-1 just 42 seconds into the first period.
Simon Holmstrom pick-pocketed Jakob Chychrun before Thompson got his stick on a 2-on-1 try at 6:45.
Wilson gave Washington a 1-0 lead at 7:37 on the power play. Ovechkin sent a no-look pass to Wilson, who redirected the pass over Sorokin’s glove.
At 9:32, Thompson stopped a Lee deflection, diving back to cover the puck with help from Dylan Strome to stop it before it trickled over the goal line.
Thompson went into the splits to deny Mathew Barzal’s wraparound try at 18:59.
Wilson scored his second of the game at 13:58 of the second period to give the Capitals a 2-0 lead. Sorokin tried to pass the puck up the boards from behind the net, but his pass went right to Wilson, who buried it into the open net.
New York outshot Washington 22-14 through the first two periods.
Horvat cut it to 2-1 on a power play at 13:43 of the third period. After Lee couldn’t bury a Ryan Pulock rebound, Horvat beat Thompson blocker side from the top of the crease for his 15th goal of the season.
Aliaksei Protas beat out an icing and made it 3-1 with an empty-net goal at 18:49 before Ovechkin scored No. 909 into an empty net at 19:29 for the 4-1 final.