Jamie Benn and Tyler Pitlick scored for the Stars, which improved 11-1-3 in their past 15 games against the Capitals and 23-2-6 against them since the start of the 1996-97 season. Dallas is 7-1-0 in its past eight games at Washington.
Nicklas Backstrom had a goal and an assist, and Brett Connolly and Evgeny Kuznetsov scored for the Capitals (5-4-3). Holtby, who stopped Tyler Seguin on a penalty shot 59 seconds into overtime, made 32 saves.
The Capitals, who began a five-game homestand, have yet to win consecutive games this season and have one victory in their past four games (1-2-1).
"We've been turning a lot of pucks over lately and sometimes you've got to chip it in the corner and go get it, take the body, keep it a little more simple and when the play is there, you make it," Connolly said. "We're a little off on that right now, but we'll find it. We're too good of a team not to."