Washington trailed 4-1 late in the second before Alex Ovechkin scored in the final minute of the period. Dmitry Orlov scored 1:51 into the third to make it 4-3, and Ovechkin tied it at 10:15 with his 29th goal.
John Tavares scored twice, including his career-best 31st goal, and added an assist, Matt Moulson netted his 30th of the season, and defenseman Travis Hamonic also scored for the Islanders (28-31-11), who lost their third straight game in heartbreaking fashion.
The Capitals (36-28-6) have won four in a row and lead ninth-place Buffalo by four points in the Eastern Conference playoff race.
Moulson gave New York a 1-0 lead 8:54 in when his slap shot deflected off the glass behind the net and then dropped in by goalie Michal Neuvirth. Moulson has scored 30 goals in three consecutive seasons, the first time an Islanders player has done that since Ziggy Palffy (1996-98).
Hamonic's power-play tally, his second goal of the season, from Tavares and Frans Nielsen at 19:39, made it 2-0, and Tavares scored at 9:05 of the second on the power play to push the lead to three. Hamonic also had two assists for the first three-point game in the NHL.
Mike Knuble scored his fourth goal of the season 28 seconds later to bring the Capitals within 3-1.
Tavares scored his second of the game at 11:44 of the second period with a snap shot from the right circle to beat Neuvirth, who still managed to improve to 5-0 against the Islanders.
Orlov got the Capitals closer, and Ovechkin made it 4-4 when he knocked a rebound of Keith Aucoin's slap shot past goalie Evgeni Nabokov. Aucoin had three assists.
New York won the first two meetings with the Capitals and were leading 2-0 in the third matchup on Feb. 28 with less than four minutes left in regulation. But Troy Brouwer scored twice, and Ovechkin won it in overtime.
The Capitals began a five-game trip as they try to improve their playoff positioning. Since Feb. 18, Washington had lost three straight, won three in a row, and lost another three consecutively before this most recent three-game winning streak.
The Islanders had back-to-back demoralizing losses over the weekend. New Jersey scored two goals 14 seconds apart in the final 1:39 on Saturday to beat the host Islanders 2-1 at Nassau Coliseum. The next night, they lost at Madison Square Garden when Rangers forward Marian Gaborik scored a power-play goal to win it in the closing seconds of overtime.
NOTES: Islanders RW P.A. Parenteau sat out because of an undisclosed upper body injury. ... The Capitals were without forward Nicklas Backstrom (concussion) and defenseman Tom Poti (back). Defenseman Mike Green served the last of a three-game suspension. . The three points for the 21-year-old Tavares left him one point shy of becoming the first Islanders player to have at least 70 in a season since Alexei Yashin had 75 in 2001-02.