Gaudreau then scored at 4:49 of the first when a defensive breakdown in the neutral zone between Capitals defensemen John Carlson and Brooks Orpik left him all alone on the right wing. Gaudreau beat Holtby to his blocker side off the rush to make it 1-1.
Gaudreau has 19 points (eight goals, 11 assists) during his streak. The Flames have won nine of 10 when Gaudreau has a multi-point game.
"What a coach likes more is his backcheck on [Capitals forward Alex Ovechkin] that lifted the stick," Flames coach Glen Gulutzan said of Gaudreau. "I know he's going to get points because he's just that gifted, but his commitment to winning just shows itself night in, night out. I love that he's on the roll. You want him to stay on the roll."
Monahan gave Calgary a 2-1 lead at 5:22 of the second period. It was his seventh goal in his past eight games against Washington.
Holtby stopped Gaudreau short-side at the left post, but couldn't find the puck underneath his pads. Monahan did and scooped it into the net.
Backlund scored at 4:38 of the third period during a delayed penalty with the Flames playing 5-on-4. The goal made it 3-1 and gave them another power play after Alex Chiasson slashed Jaromir Jagr.
Giordano scored on a wrist shot from the point after Chiasson's penalty expired to make it 4-1.
"We continue like that, then we're going to continue hovering around .500," Eller said. "Win a game here and there. We've got to play with a lot more determination. The playoff race is tight. It's November, but the playoff race is right now."