St. Louis added an assist, while Vincent Lecavalier and Cory Conacher also scored goals for the Lightning.
Joel Ward scored twice and Wojtek Wolski also had a goal for the Capitals, who lost in Adam Oates’ NHL coaching debut.
“I think some of the mistakes came from conditioning,” Oates said. “We got tired at times. The game went in waves.”
St. Louis’ drive from above the left circle during a 5-on-3 power play gave Tampa Bay a 4-3 advantage at 4:47 of the third.
“5-on-3, at that time of the game, you’ve got to score,” St. Louis said. “If you don’t score, it might haunt you.”
Conacher, who had an assist in his first NHL game, scored his first goal to extend the lead to 5-3 with 6:36 to go. Brewer scored his second goal late in the third.
The announced crowd for the first Tampa Bay home game this season was a sellout of 19,204.
The Lightning went ahead 3-2 on St. Louis’ power-play goal from the low slot off a pass from Lecavalier at 5:11 of the second. St. Louis has 25 goals and 71 points in 69 career games against Washington.
Wolski made it 3-all while both teams had a player in the penalty box with 1:45 left in the second.
Ward scored his second goal to tie it at 2 just 1:59 into the second during a delayed penalty. The right wing didn’t have a goal in his final 13 games last season.
“You always hope to contribute, for sure,” Ward said. “You’re not going to go out there and say I’m going to score five or anything, but you try to finish your opportunities if you can. I was fortunate to get a couple.”
Tampa Bay took a 1-0 lead when Brewer stopped a personal 50-game goal drought from the top of the left circle at 6:24 of the first.