Beaupre, winning his 18th game of the season, stopped shots with his stick, gloves and pads; he made diving saves, sliding saves and lunging glove saves. In all, he stopped 33 shots.
The only shot to elude him was during a power play in the third period. Former Philadelphia Flyer Brian Propp scored on a shot from the left circle that caromed off the far post and into the cage behind Beaupre.
"Beaupre came up real big for us," said Capitals coach Terry Murray. "He was really sharp tonight. Our defense played well, especially in the first two periods, but whenever we made a mistake, Donnie was there for us."
Beaupre said: "The team played solid hockey last night [in Thursday's 6-2 win over the Islanders] and came back and played another solid game tonight. It would have been nice to get a shutout, but I really can't complain because the only goal they scored was a good goal."
The victory moved the Capitals into third place in the Patrick Division past the idle New Jersey Devils. Washington has won two in a row and is 8-2-3 in its past 13 home games.
"If feels good to finally be over .500 [35-34-6]," said Murray. "Also, we're back in third place. It took a lot of hard work, patience and staying focused on the job at hand. I couldn't be happier with the intensity, attention to detail and togetherness of this club."
The North Stars pulled goalie Jon Casey with 75 seconds remaining in favor of a sixth attacker.
The Capitals took a 2-0 first-period lead on a power-play goal and a fluke goal. Calle Johansson had a hand in both scores.
Kevin Hatcher gave Washington a 1-0 advantage with an extra-man goal at 14:21. His slap shot from center point found its way through Casey's pads, with Johansson getting the assist.
With one minute remaining in the period, Johansson fired a shot from outside the blue line. Casey got his stick on the puck but could not control it, and the puck caromed off and into the cage. It was a shot that most goaltenders, Casey included, save 99 times out of 100.
Washington's lead rose to 3-0 at 12:29 of the second period on Steve Leach's goal. Kelly Miller carried the puck across the blue line and left a drop pass for Leach at the right point. His slap shot beat Casey low and to the left side.