Galchenyuk put the Coyotes up 1-0 at 2:09 of the first period when he put in a rebound in the slot from Riley Nash's shot.
Chychrun made it 2-0 at 4:21 when he directed a pass from Phil Kessel toward the net that got past Mrazek, who went down and was unable to get across the crease. Toronto challenged for offside, but the goal was upheld after video review.
Travis Boyd extended the lead to 3-0 at 1:08 of the second period when he swatted the puck out of the air behind the goal line and banked it off Maple Leafs defenseman Timothy Liljegren in the crease.
Pierre Engvall cut it to 3-1 at 4:55 when he put in a loose puck in the crease.
Christian Fischer made it 4-1 at 11:57 when he shot over Mrazek's glove in the high slot.
"We gave ourselves a chance, and Erik gave us a chance in there, so we battled back, got a point, but obviously tonight is just not good enough from the start," Matthews said. "We didn't get playing until the third period."
Kessel had an assist in 17:25 in his 957th consecutive NHL game after playing one shift in a 9-2 win at the Detroit Red Wings on Tuesday before leaving to fly back to Arizona to be with his wife for the birth of their child.
"I don't want to sit out," Kessel said. "I've had injuries, I could have sat out many a time, but I just don't want to be in the stands. I love to play the game and I don't want to not be out there. I always try to play no matter what, so I was fortunate I was able to play."
NOTES: Maple Leafs forward Mitchell Marner had his eight-game point and assist streak end. He scored 17 points (six goals, 11 assists) in the run. … Chychrun has scored 10 points (five goals, five assists) in the past six games. … Coyotes forward Nick Schmaltz had an assist and has scored 12 points (four goals, eight assists) in the past three games. … Arizona forward Clayton Keller had an assist to increase his point streak to four games (nine points; three goals, six assists). … Maccelli had his first two NHL assists. … Kallgren was recalled from Toronto of the American Hockey League on Thursday on an emergency basis after goalie Jack Campbell sustained a rib injury in a 6-4 win against the Seattle Kraken on Tuesday. Campbell will be out at least two weeks. Kallgren was selected in the seventh round (No. 183) by the Coyotes in the 2015 NHL Draft. … Toronto has used five goalies this season (Mrazek, Campbell, Joseph Woll, Michael Hutchinson, Kallgren) to tie its 1983-84 record for most in a season. ... Kessel started his streak on Nov. 3, 2009 with the Maple Leafs and played the first 446 games of it for them (through 2014-15).