The Capitals have won two in a row and six out of eight, while giving the Lightning their sixth straight loss. Tampa Bay's streak is the longest currently working in the NHL.
Washington built a 3-0 lead early in the second period, with Brouwer scoring twice after Alex Ovechkin gave the Capitals the lead 3:52 into the game.
Tampa Bay rallied within 3-2 with 3:24 to play on a power-play tally from Steven Stamkos, whose 30 goals lead the league.
Brouwer completed his hat trick with an empty-net goal that came with a minute remaining in regulation. It also turned out to be the game-winner when Tampa Bay's Vincent Lecavalier scored with 11 seconds to go.