Auston Matthews scored to make it 4-3 with 8:00 left, but Oshie scored 59 seconds later for a 5-3 lead. Tyler Bozak made it 5-4 with 27 seconds left and Toronto using an extra attacker.
"It's nice that we're able to score goals and get ourselves back in the game, but we didn't play near as good as we needed to," Maple Leafs coach Mike Babcock said. "We talked a lot about how the game was going to be today, but it didn't look like any of that sunk in. We weren't good enough, we didn't compete hard enough. I thought they won all the battles and all the races."
Oshie gave the Capitals a 1-0 lead at 2:58 of the first period, and Ovechkin made it 2-0 1:36 later on the power play. The Maple Leafs scored 42 seconds later when Jake Gardiner's point shot deflected off Zach Hyman's skate at the top of the crease and slipped past Holtby's left pad.
Tom Wilson scored at 13:41 and 16:04 to put the Capitals ahead 4-1. He has three goals in the series after scoring seven in 82 regular-season games.
James van Riemsdyk scored a power-play goal at 5:39 of the second period to make it 4-2.
Oshie's goal at 8:11 of the third period was waved off when it was ruled Nicklas Backstrom interfered with goalie Frederik Andersen.