Holmberg tied it 1-1 at 9:02, tipping in Timmins' shot from the left point on a power play.
Jarnkrok put the Maple Leafs in front 2-1 at 12:33 with another power-play goal, this one coming off a pass from Timmins.
"We let them back into the game too many times and just didn't close tonight," said Timmins, who was traded by Arizona to Toronto on Nov. 23 for forward prospect
Curtis Douglas
.
Jakob Chychrun tied it 2-2 at 6:52 of the second, scoring five-hole off a Nick Ritchie rebound six seconds into a Coyotes power play.
Kerfoot gave Toronto a 3-2 lead at 11:19 of the second period, putting in the rebound of Giordano's shot following a solo rush into the offensive zone.
"Obviously, we didn't do the job on the penalty kill, so that was a bit frustrating, but we regrouped," Bjugstad said. "This team is relentless, and we find a way to be in it. And now we're finding ways to win, especially at home."
Arizona is 7-3-2 at Mullett Arena, including 6-1-1 in December.
"We're a hard team to play against, and teams don't like coming into the Mullett," Bjugstad said. "It's a different rink to play in for a lot of people, and we're trying to use it to our advantage. We're having some fun with it."
NOTES: It was McBain's first multigoal NHL game. He played collegiately at Boston College, and with the Eagles playing against Arizona State this weekend, many of his former teammates were in attendance. ... The Coyotes, who also defeated the Maple Leafs 4-2 on Oct. 17, have won four straight and six of eight (6-1-1) against the Maple Leafs. … Toronto also blew a third-period lead against the St. Louis Blues on Tuesday but came back to win 5-4 in overtime. ... Forward Dryden Hunt had one shot and six hits in 8:10 of ice time in his Maple Leafs debut. He was acquired in a trade with the Colorado Avalanche for forward Denis Malgin on Dec. 19. … Vejmelka is 3-0-0 against Toronto. … Rielly returned after missing 15 games with an upper-body injury.