The Avalanche lost defensemen Erik Johnson and Anton Lindholm to upper-body injuries. Johnson needed help off the ice at 1:59 of the third period; Lindholm left with 3:40 remaining in the second.
"The couple injuries in the back end could hurt us more than just the loss today," Avalanche coach Jared Bednar said.
Strome gave the Oilers a 3-2 lead at 13:18 of the third period from the slot off a pass from Michael Cammalleri for his first goal in 22 games. McDavid completed his hat trick with an empty-net goal with 1:26 remaining.
The goal was especially sweet for Strome, who was visibly upset after Varlamov extended his left pad to stop him at 8:02 of the third.
"He's a great goalie," Strome said. "He makes some spectacular saves, he's got those long legs so I couldn't get that one up there enough. Obviously frustrating, but you got to keep with it, and then you get another chance and luckily it went in. Hopefully the piano is off my back a bit now."
The Oilers tied the game 2-2 on McDavid's second goal and 25th of the season at 8:59 of the third. He beat a screened Varlamov from the right face-off circle.
"There's no excuse for the third," Bednar said. "We played 14 minutes and had three shots on goal in a game we're trying to win and need to win at home. No excuse for that.