WASHINGTON -- Washington Capitals coach Barry Trotz was worried about Monday night's contest being a "trap game."

It almost was, but Washington escaped.

Defenseman John Carlson scored with 46 seconds left in overtime as the Capitals rallied from a two-goal deficit to defeat the Arizona Coyotes 3-2.

Evgeny Kuznetsov fed T.J. Oshie in the slot, but Oshie fanned on the shot. The puck sailed over to Carlson, who beat goalie Scott Edgewood for his first goal of the season after Washington kept a Coyotes trio pinned in its own end and unable to get a change.

"I thought Lars Eller wore that unit out for about a minute and then we were able to get a real smart change," Trotz said. "And then they were trying to exit the zone, and a real huge play by T.J. Oshie to keep that puck alive, and we were able to transition and it ends up in the back of the net."

Earlier in the game, Carlson had an assist. Alex Ovechkin scored his 12th goal of the season for Washington (8-6-1), and Davante Smith-Pelly added a goal.

Braden Holtby made 24 saves as the Capitals won a third consecutive game for the first time this season.

"We're just kind of finding our way, figuring out what's working for us," said Carlson, who leads the league in ice time per game. "We've gotta put a couple of these together. We didn't start (the season) like we wanted to, so we've got a lot of work to do."

The Coyotes (2-12-2), looking for their first back-to-back wins of the season, took a 2-0 lead on their first two shots on goals by rookie Clayton Keller (11th of the season) and Christian Fischer (fourth).

"We're gonna keep (working) the process, keep pounding away," Arizona coach Rick Tocchet said. "It's a hard-earned point against a tough hockey club."

Trotz had warned the Capitals not to take the Coyotes lightly.

"I viewed this in some ways as a little bit of a trap game because you may look at their record, but your eyes tell you that's a much better team," Trotz said of the young Coyotes. "They're gonna be pretty dynamic."

Wedgewood finished with 37 saves as Washington went 1 of 6 on the power play.

"It's tough, that's a potent power play, so you don't want to give them five or six power plays," Tocchet said. "The slashing, the hooking, you can't do that against this team."

It took all of one minute for Arizona to jump in front. Keller took advantage of an Eller turnover at the Coyotes' blue line, went the other way and came in on Holtby as part of a two-on-one. When the defenseman didn't commit, Keller kept the puck and fired low to make it 1-0.

Keller, 19, has collected a point in 14 of his 19 career NHL games (11-8-19).

Arizona doubled its lead at 6:42 when Christian Dvorak got behind the defense on the rush along the right boards. Fischer, driving to the net, deflected the centering pass under the crossbar on Holtby's stick side.

"You're sitting there, you're playing pretty well and you're down 2-0," Trotz said. "I'm looking up and I'm going, 'Just stay the course.'"

Washington cut the deficit in half when Smith-Pelly gathered in the rebound of Eller's shot and backhanded a shot past Wedgewood from just inside the left circle at 8:41 of the first period.

The Capitals have struggled on the power play early in the season -- especially at home -- and they looked bad on their first four chances, including their first three in the second period.

Then on their fourth try in the second, a Coyotes player lost his stick and Carlson set up Ovechkin for a blast from his office in the left circle that tied the score at 14:23.

"We did a wonderful job on the PK," Wedgewood said. "Ovechkin's a good shooter, but I don't like the way I played that. I was a little deep."

Holtby kept things tied up when he stoned Brendan Perlini on a breakaway with 2:30 left in the second period.

NOTES: With his 216th career power-play goal, Washington LW Alex Ovechkin passed Joe Nieuwendyk for sole possession of 12th place on the NHL's career list. ... Capitals C Lars Eller has seven points (three goals, four assists) in his last five games. ... The Coyotes have scored first in 12 of 16 games this season, the best rate in the league. ... Both teams play the second of back-to-backs Tuesday night, with Washington at Buffalo and Arizona visiting Pittsburgh. ... Capitals G Braden Holtby has 199 career wins.