After Washington goalie Ilya Samsonov made a play on the puck and left it behind his net for Capitals defenseman Justin Schultz, Smith beat Schultz to the puck and tucked it inside the left post.
"I kind of circled back into the zone, they had a goalie set behind the net," Smith said. "I don't know if there was a miscommunication between the two, it kind of looked like it. But I just tried to jump on it, and it seemed like I created a little bit of a turnover there and that gave me just enough time to get it.
"But it was a great feeling. Anytime you can end one like that."
Tuukka Rask made 35 saves for Boston, which took the lead in the best-of-7 series. The Bruins are the No. 3 seed in the MassMutual East Division.
Samsonov, playing for the first time since May 1, made 40 saves for Washington, which is the No. 2 seed. He had been on the taxi squad and was removed from NHL COVID-19 protocol Saturday.
"He was huge tonight for us," Capitals defenseman John Carlson said. "I wouldn't say anything other than, 'Keep your head up, there's a lot more hockey to be played.' He did a great job for us tonight. If he didn't stand on his head, we probably wouldn't have gotten to that point. I think he should know that, but that's definitely something we'll talk about."
Game 4 is here Friday (6:30 p.m. ET; NBCSN, SN360, SNE, SNO, SNP, TVAS, NESN, NBCSWA).
Teams that win Game 3 after a best-of-7 series is tied 1-1 are 223-107 (67.6 percent) winning the series, including 3-1 in the first round last season.
The Capitals won Game 1 3-2 in overtime on Saturday, and the Bruins won Game 2 4-3 in overtime on Monday.