Sliding to the ice and snapping his glove shut, Martin Brodeur made up for a poor third period.
The Devils gave up a 3-0 third period lead while Brodeur found himself fooled by some deft Washington passing.
But his save on the crafty Ovechkin was a beauty, and Patrik Elias scored at the other end to cap a 2-0 New Jersey decision in the shootout.
Ilya Kovalchuk also scored in the shootout after netting a goal in regulation for the Devils, who have won five of their last six. Alexander Urbom and Adam Henrique added goals and Brodeur finished with 22 saves to earn the win.
Jason Chimera had the last two goals for Washington, including the equalizer with 1:42 remaining. Brooks Laich also scored while Michal Neuvirth had 25 saves for the Capitals, who have dropped three of five.
The Devils improved to 8-1 in shootouts this season, including six straight wins. The Capitals fell to 1-2 after their first shootout since November 12.
Ovechkin started a tic-tac-toe play on the left wing that finally got the Capitals on the board 3:48 into the third period. His pass found Dennis Wideman on the right side, and Wideman tapped the puck down low to Laich for the goal to get Washington within 3-1.
Later, after the Devils hit a post at the other end, Chimera got the puck to Brodeur's left and carried it around to the front of the net, hammering it in to get the Caps within 3-2 with 7:16 remaining.
He was on the same side less than six minutes later when Alexander Semin threw a shot on net and Laich ended up with the puck, spinning around to deliver a deft backhand pass to Chimera for a wide-open goal into the right side of the net.
On a power play in the second period, Kovalchuk ripped a slap shot past Neuvirth from the point to give the Devils a 1-0 lead, touching off a three- goal burst in under eight minutes.
Urbom, who had one goal in eight games last season, scored for the second time in the NHL after taking a pass in the slot and sending Neuvirth to his stomach with a deke to his forehand. He flipped the puck over the goaltender's stick.
Henrique made it 3-0 midway through the period after deflecting a point shot from Matt Taormina.
The Capitals couldn't get past the .500 mark under Dale Hunter. They are 5-6 since he took over as head coach on November 28.