GLENDALE, Ariz. -- Calgary general manager Brad Treliving cited his club's special teams play as a key issue in the Flames' 5-10-1 start this season.

That area is no longer a problem.

Mikael Backlund, Troy Brouwer and Kris Versteeg scored power-play goals, and a shaky Brian Elliott made 25 saves in his first start in nearly a month as the Flames snapped a two-game losing streak with a 4-2 win over the Arizona Coyotes on Monday night at Gila River Arena.

Arizona had allowed just three power-play goals on home ice all season -- the fewest in the league -- but the Flames went 3 of 6 with the man advantage. They have at least one power-play goal in eight straight games for the first time since 2005, and they have produced 13 power-play goals during that stretch.

"We talked about it when we were taking a little water early that we'd have patience and we'd get out of it and our special teams would improve, and they have," Calgary coach Glen Gulutzan said. "That's one piece of the puzzle in this league is the specialty teams game, and you can see what happens when you win it."

Versteeg took a soft pass from Sean Monahan at the right of the net and pushed a puck past Mike Smith (24 saves) for the winner at 12:25 of the third period.

It was the fifth goal of the season for the veteran of two Stanley Cups with Chicago, who signed a one-year deal with Calgary in October. It also came after he left the ice in the second period for a concussion test after taking a Jamie McGinn elbow to the head.

"The last thing on my mind was scoring the game-winning goal," Versteeg quipped. "I definitely had my bell rung."

Calgary killed off a five-on-three Arizona power play late to preserve the win. The Flames' penalty-killing unit has thwarted 31 of opponents' past 35 chances (88.6 percent).

Christian Dvorak put the Coyotes on top off a fortunate bounce early in the first period.

Elliott went behind his net to stop and clear a puck along the boards, but his pass hit Coyotes left winger Josh Jooris, a former Flame, in the chest. The puck bounced onto Dvorak's stick, and the center tucked it in the open side of the net for a 1-0 lead at 5:12 of the first period.

The Flames did not take their first shot of the first period until Backlund's attempt with 8:15 remaining, and Arizona outshot Calgary 15-7 in the period, but Calgary evened the score at 8:10 of the second period.

With McGinn in the box, defenseman Dougie Hamilton found Backlund open in front of the net for the equalizer. Calgary also flipped the shot script in the second period, holding Arizona without a shot until 1:39 remained in the period and outshooting the Coyotes 12-2.

"We made mistakes to put them on the power play, so that's the biggest one," Arizona coach Dave Tippett said. "When you can't kill them, that complicates things a lot."

Brouwer scored just 20 seconds into the third period when he took a feed on the right wing from Johnny Gaudreau and blew a shot past Smith for a 2-1 lead.

The Coyotes answered when Ryan White's shot from the half-wall somehow trickled through Elliott and in at 9:07, but Versteeg scored with Shane Doan in the penalty box for elbowing.

"You can't give them the chances that they got," Doan said. "We had our power-play chances and didn't score. That's the way it goes."

T.J. Brodie added an empty-net goal for Calgary with one minute remaining.

NOTES: Flames G Brian Elliott made his first start since Nov. 28 against the New York Islanders in Brooklyn. Since signing a three-year, $7.5 million deal this summer to leave St. Louis, Elliott has struggled and lost his starting job to Chad Johnson. "Brian's a good goalie, and Brian's going to be a big part of us as we go forward here," GM Brad Treliving said. "We're going to need Brian this season." ... The Coyotes moved rookie LW Lawson Crouse onto the top line with C Martin Hanzal and RW Radim Vrbata. ... The Coyotes scratched rookie LW Brendan Perlini, who has two goals and three points in eight games, and rookie D Anthony DeAngelo, who has three goals and nine points in 16 games. ... The NHL's roster freeze went into effect at midnight and ends Dec. 28 at midnight. ... The Flames recalled D Tyler Wotherspoon on Monday morning.