It was Holtby’s fourth shutout of the season and second against the Jets. He also blanked Winnipeg 3-0 on March 2, the only previous time Winnipeg was shut out this season.
Ondrej Pavelec faced 25 shots as the Jets (16-13-2) had their home winning streak snapped at three.
Winnipeg remained in first place in the Southeast Division and the third seed in the Eastern Conference, two points ahead of the Carolina Hurricanes, who lost 4-1 to New Jersey on Thursday night.
The Jets and Capitals face off again Friday night in Winnipeg.
The Jets were on their second power play early in the third, but Brooks Laich got control of the puck and was stopped on a breakaway by Pavelec.
Kane and Antti Miettinen challenged Holtby on a two-on-one midway through the period, but the netminder snapped out his right leg and stopped Miettinen’s shot.
Pavelec took a delay of game penalty late in the third period and it proved costly.
Brouwer opened the scoring with a wrist shot from near the bottom of the faceoff circle that beat Pavelec at 3:06 of the first period, extending his points streak to three games (two goals, two assists).
Laich assisted on the goal for his first point of the season after making his season debut Tuesday following a lengthy groin injury.
Jets forward Evander Kane had a good opportunity late in the period when he found himself alone in front of the net, but he couldn’t get his stick on the puck to make a shot.