Brooke Nelson, Casey Cesikas and Josh Bailey also found the box for the Islanders, who drew 14-1-2 at home.
The victory saw them join the capitals and Pittsburgh at the top of the Eastern Division standings with 50 points. Capitals have a match on hand for both of these teams.
Goalkeeper Simeon Varlamov fired 22 pucks for the islanders, raising his record to 8-3-1 in his last 12 decisions. During this streak, he conceded 30 goals. His cumulative record is 15-7-3.
In the loss, defender John Carlson scored twice. Complete TJ Oshie and Daniel Sprong.
The match was marked by an initial chaotic period, beginning with an incident involving Capitals goalkeeper Ilya Samsonov, who was forced to leave the ice after 30 seconds of play when he collided with Ushi behind his net.
Oshi’s shoulder contacted Samsonov’s head. Vitek Vanesk temporarily took over.
Samsonov returned to the net just over three minutes before the end of the period, before Nelson scored his thirteenth goal of the season at 5:32 pm to make it 3-1.
Sprung closed the gap after just 48 seconds before Barzal scored his second goal of the match at 18:53 thanks to a goal from an almost impossible angle.