Dzingel, playing for the first time since Dec. 10, scored for the first time since Nov. 20.
He gave the Coyotes a 1-0 lead at 14:57 of the first period by scoring off a rebound of his shot that deflected off the end boards.
"It's the first shot I've had in a while and I shanked one high and then I got lucky, it was a really good bounce," Dzingel said. "I haven't had a lot of good bounces, so it's nice to have."
The Maple Leafs couldn't get the puck past Vejmelka in the first two periods despite outshooting the Coyotes 35-12.
"It's always better for you early to see so many shots, so I got to where I felt really good," Vejmelka said. "My team helped me, and it was a big day for us today."
Matthews tied it 1-1 14 seconds into the third period when he adjusted the puck on his stick to shoot it around defenseman Shayne Gostisbehere from the left circle for his 24th goal of the season.
Matthews' fourth goal in three games came before a large group of friends and family, including his parents, from nearby Scottsdale, Ariz., where he grew up, but the Maple Leafs couldn't get the tying goal.
"Certainly we had our looks, our opportunities," forward John Tavares said. "It's just one of those nights where you got to find a way to break through and, unfortunately, we didn't. We've got to do a better job of winning some third periods."
The Coyotes were without coach Andre Tourigny, two assistant coaches and five players, four of them defensemen, who are in NHL COVID-19 protocol. Assistant coaches Phil Housley and Cory Stillman ran the team.
"I know they've got a lot of guys that are injured and in COVID protocol, but obviously [Vejmelka] stepped in and played really well," Matthews said.
NOTES:Matthews has scored 13 points in the streak (11 goals, two assists) dating to Nov. 24 and 22 points (16 goals, six assists) in his past 14 games. … The Maple Leafs, who had points in their previous six games (5-0-1), failed to match their record for fewest games to reach the 50-point mark, set in 35 games in 1946-47. … Mrazek's start was his first since Dec. 11. … Toronto was 11-2-2 in its previous 15 games. … Dzingel also scored Nov. 18 against the Columbus Blue Jackets after coming off a 10-game injury layoff. … Coyotes defenseman Vladislav Kolyachonok had a game-high seven hits in 12:01 in his NHL debut. … Vejmelka is 4-13-1 this season. His NHL career high in saves is 46 (1-0 win at the Winnipeg Jets on Nov. 29, and 3-1 loss to the Jets on Jan. 4).