Alex Ovechkin, T.J. Oshie and Justin Williams scored for Washington, which trails the best-of-7 series 3-2 and will try to extend it again by winning Game 6 at Pittsburgh on Tuesday (8 p.m. ET; NBCSN).
"We didn't want to give up," Ovechkin said. "It doesn't matter what kind of position we are [in]. We knew we have to do it. Forget it and next one is a big one, I think, with our team and with our group. We can't stop."
Chris Kunitz scored for Pittsburgh, which had won three in a row. This was the first game in the series decided by more than one goal.
"We'll put the game behind us, but nothing is easy," Penguins coach Mike Sullivan said. "This is a hard league. It's hard to win. We're playing against a really good team. We think we're a really good team. But as far as the game is concerned, for us we [have to] have a short memory."