Brouwer's tallies gave Washington a 2-0 lead by early in the second period and the Capitals never looked back in winning for only the third time in 12 games to start the season.
Mathieu Perreault and Joel Ward each added a goal and an assist. Holtby turned aside all 27 shots he faced in logging his fourth career whitewash.
Florida's Jose Theodore started in net and was torched for five scores on 21 shots before pulled midway through the third period.
Scott Clemmensen relieved and stopped four shots the rest of the way for the Panthers, who were coming off a Thursday win over Philadelphia.