Holtby made 28 saves for the Capitals (3-3-0).
"[Andersen] was great and so was Holtby," Brown said. "I think we gave up more than we'd like, but we did a lot of good things to get through the neutral zone and hang on to pucks. It was good to find one there."
Washington forward Tyler Graovac, in the lineup to replace center Lars Eller (illness), left the game in the first period with an upper-body injury after he was hit by Toronto forward Matt Martin on two shifts. Graovac is expected to miss some time, Capitals coach Barry Trotz said.
It was the first game between the Maple Leafs and Capitals since Washington won in six games in the 2017 Eastern Conference First Round.
"When it's crunch time and you're getting close to the end of the year like we were last year, you look back on these kind of close games and think about the value that's in these points," Rielly said. "To get these ones and get rolling a little bit is a great feeling. But it's only six games."