Washington appeared to take the lead on Justin Schultz's sharp-angle shot at 14:06, but New York successfully challenged for offside and the clock was reset to 6:08 remaining.
Palmieri gave the Islanders a 2-1 lead with 2:58 left. Josh Bailey deked around defenseman John Carlson in the left circle, skated toward the net and passed to Palmieri at the right post for a tap in.
Ovechkin, who has scored 37 goals this season, trails Wayne Gretzky (894) and Gordie Howe (801) in NHL history.
"He's got a lot of game left in him," Laviolette said of the 36-year-old. "He's got a lot of time, a lot of game. He is in great shape, he's strong. He continues to fire the puck and he continues to produce."
NOTES: Varlamov played three seasons for the Capitals (2008-11). ... Palmieri has scored nine points (five goals, four assists) in his past nine games. ... Islanders forward Jean-Gabriel Pageau had an assist to extend his point streak to five games (six points; one goal, five assists) and nine of 10 (11 points; three goals, eight assists). ... Kuznetsov extended his point streak to six games (nine points; four goals, five assists). ... New York was 0-for-1 on the power play, and Washington has killed 31 of 34 dating to Feb. 13 (12 games).