The Red Wings were without forwards Tyler Bertuzzi (upper-body injury) and Robby Fabbri (knee); the Capitals were missing defenseman John Carlson (lower body), and forwards T.J. Oshie (lower body), Nicklas Backstrom (hip), Connor Brown (knee) and Tom Wilson (knee).
Detroit appeared to take a 2-1 lead at 17:42 on Larkin's rebound, but David Perron was ruled to have interfered with Kuemper.
Copp scored his first goal with the Red Wings at 16:10 of the third period, tapping Adam Erne's pass under Kuemper to make it 2-1.
"I got off to a slow start in the goal column, but maybe this will open the floodgates," he said. "I thought we battled and made the kind of desperate plays you need in a game like this."
Larkin scored an empty-net goal with 28 seconds left for the 3-1 final.
NOTES: Ovechkin has 36 points (23 goals, 13 assists) in 31 career games against the Red Wings. … Gordie Howe's son, Mark Howe, attended the game as part of the 25th anniversary celebration for the 1997 Red Wings, who ended their 42-year championship drought.