The Jets were trying for what would have been their fourth straight victory and had a one-goal lead heading into the third period.
The goal for Ovechkin, which gave the Capitals a 3-2 lead, was his league-leading 40th of the season. Toronto's Phil Kessel began the night in second place with 30 goals.
Brouwer had two scores in the game, having given Washington the lead 4:46 into the contest. Bryan Little and Dustin Byfuglien scored the goals that put Winnipeg in front heading into the third period.
Braden Holtby turned aside 34 shots to collect the victory. Ondrej Pavelec stopped 26-of-30 shots for the Jets.