Conor Sheary scored, and Ilya Samsonov made 22 saves for the Capitals (44-24-12), who remained one point behind the Pittsburgh Penguins for third place in the division with two games remaining. The Penguins have one regular-season game left after a 5-1 loss to the Edmonton Oilers on Tuesday.
Washington, which has lost three of its past four games (1-1-2), played without forward Alex Ovechkin because of an upper-body injury sustained during a 4-3 shootout loss to the Toronto Maple Leafs on Sunday.
"We can't play like we did tonight going into the playoffs," Capitals coach Peter Laviolette said. "This isn't who we are. This isn't our M.O. It's one night, it was lousy and so that's that."
Ilya Sorokin made 32 saves for the Islanders (36-34-10), who had lost five straight (0-4-1). They played with 11 forwards after center Brock Nelson was a late scratch because of a non-COVID-19 illness.
New York will host Washington on Thursday.
"To me it was a [heck of a] team win," Islanders coach Barry Trotz said. "Our room is hacking and coughing and there's a lot of guys sick, and right now they're battling through it. Give them a lot of credit; I thought it was a good character win."