Anderson played four regular-season games, starting two, including May 8 when he made 28 saves in a 2-1 overtime win against the Philadelphia Flyers. He turns 40 on Friday.
"Just to get that game, I was able to stay a little fresh and kind of jump-start the engine there, just kind of reinforce that you do need to be ready and you're one shot, one play away from being the guy in the net," Anderson said.
Anderson is 12-5 in overtime in the NHL playoffs, including 4-1 against the Bruins.
"Tough spot, I think, to put somebody in, but Andy's answered the bell really his whole career, but he's answered it for us when we needed him," Capitals coach Peter Laviolette said. "He truly epitomizes the concept of working hard every day so that when you get your opportunity, you're ready, and that's exactly what he did."
Tuukka Rask made 29 saves for Boston, which is the No. 3 seed in the MassMutual East Division.
"It was a one-timer from the blue line there," Rask said of Dowd's goal. "I think it was going over my head or at my head or something, then hit a stick, hit my chest and somehow ended up in the net. I think I probably bumped it into my own net."
Game 2 of the best-of-7 series will be played here Monday (7:30 p.m. ET; NBCSN, CBC, SN, TVAS, NBCSWA, NESN).
"Our offensive game was just not where it needed to be tonight," Bruins coach Bruce Cassidy said. "I thought our power play (1-for-4) wasn't crisp. It bled into our 5-on-5. At the end of the day, not enough on the offensive side of things. We weren't hard enough to play against."