WASHINGTON -- Washington Capitals coach Barry Trotz had some pretty simple advice with his team trailing the Boston Bruins 2-0 after the first period Thursday night.

"The No. 1 thing (I said) was 'let's pass to the guys in red,'" Trotz, referring to Washington's sweater color, told his team, which had lost three straight and was on the verge of setting a team record for a scoreless streak.

Washington proceeded to rally from 2-0 and 3-2 deficits, and Alex Ovechkin scored the only goal of the shootout to give the Capitals a 4-3 win over the Bruins.

It was the Caps' 12th straight victory over Boston.

Ovechkin, who missed his attempt in Wednesday's 1-0 shootout loss to the Rangers, was Washington's third shooter. He made a move to his right and fired high over Boston goalie Anton Khudobin, and Boston's Riley Nash failed to convert on the Bruins' final attempt.

"That's one thing that Ovi does is that if he has failure he says, 'I've got to make up for it,'" Trotz said "There was no doubt that thing was in. He delivered that with authority."

Boston had won five straight while the Capitals (23-13-3) were completing two sets of back-to-back games -- one set before Christmas and the other two games after Christmas.

"This last little stretch ... is about the toughest scheduling you're ever gonna get," goalie Braden Holtby (31 saves) said. "The last game of it, to grind out a victory like that is gutsy, it shows character, but obviously our starts have been an issue and that's something that we can work on."

David Backes' second goal of the night gave Boston a 3-2 lead at 7:19 of the third period, but Washington tied it on Brett Connolly's eighth goal of the season during a scramble in front with 8:38 remaining.

Backes had given the Bruins (20-10-6) a 1-0 lead early in the first period and Noel Acciari made it 2-0 shortly thereafter.

Lars Eller's second-period goal broke a 177:32 Washington scoreless streak and Ovechkin's 24th goal of the season tied it.

Danton Heinen had two assists for Boston and Khudobin made 31 saves. Boston went 0-for-5 on the power play.

"I felt it was probably one of our best PK nights," Washington's Tom Wilson said. "We were making good reads and making good plays and sacrificing. We shut down some pretty good players."

Washington has won seven straight at home and Holtby (14-2 in his career vs. the Bruins) has yet to lose two straight games this season.

The Bruins had their 2-0 lead before the Capitals got their first shot on goal.

First, Nash won a battle for the puck in the corner to the left of Holtby. He then sent a perfect feed into the slot and Backes one-timed the puck past Holtby for his sixth goal of the season at 1:23.

"He's a valuable asset to our team," Bruins coach Bruce Cassidy said of Backes. "He might not ever be the highest scorer here, but he hits, these types of games he gets to the net, he'll get his looks...he'll win his puck battles on the wall."

Less than a minute later, Acciari won a battle behind Holtby, came around to the goaltender's left and scored off his own rebound at 2:12.

"When you're able to get a 2-0 lead, you hope that you can step on the throat and finish them off," Backes said.

Trotz shook up his lines to start the second period, moving Devante Smith-Pelly up to the top line with Ovechkin and Nicklas Backstrom. Wilson went to the third line and Andre Burakovsky from the third to the fourth.

Eller got Washington on the board at 12:31 when he fired a wrister over Khudobin's left shoulder from high in the slot for his fifth goal. Wilson got the assist.

Less than two minutes later, with Washington on a power play, Ovechkin blasted a one-timer past Khudobin from his usual spot in the left circle at 14:07 to tie it. It was Washington's first power-play goal in over five games.

"That's always tough to defend. He can shoot it from there," Cassidy said. "You ask the other teams around the league how they defend it and it's difficult. If you overplay him, they got the slot shot, which they had some good looks from."

NOTES: According to STATS LLC, the Capitals' record for longest goal drought is 181:15 from Oct. 25, 1989, at Winnipeg, to Oct. 31, 1989, versus St. Louis. ... The Capitals assigned F Nathan Walker to Hershey of the AHL. ... Capitals D John Carlson recorded his 25th assist of the season. ... F Evgeny Kuznetsov, playing his 300th NHL game, had an assist. ... Boston C Riley Nash (assist) has five points in his last four games. ... The Bruins are 15-0-2 in games in which they have held a two-goal lead. ... Capitals head coach Barry Trotz is tied with Lindy Ruff (736) for fifth place on the NHL's all-time wins list.