The two-run homer by Brett Lawrie of Langley, B.C., the three runs batted in by Edwin Encarnacion who has 110 for the season and the solo homer by J.P. Arencibia all helped Morrow's cause.
But two defensive plays in left field by Anthony Gose were just as vital.
"When you've got good defence you have confidence in throwing strikes and letting them put the ball in play," Morrow said.
The loss cut the Yankees (90-66) lead in the American League East over the inactive Baltimore Orioles to one game and in part they can blame Gose, a centre-fielder by trade who is possibly auditioning for the starting job in Toronto's left field next season.
Gose ran down Nick Swisher's drive to left centre at the wall in the fourth. He then made a strong throw to second baseman Kelly Johnson who in turn relayed to first baseman Adam Lind to double up Robinson Cano for the inning-ending double play.
"That got us out of the inning, a great against the wall and then the throw," Morrow said.
"(Cano) probably got a bit too far but it's a great play to make," said Yankees manager Joe Girardi. "He was maybe a little aggressive but you don't want our guys being passive.
"It was a great play by Gose."
In the next inning, Gose cut off a single by Russell Martin and prevented the possibility of a double. That set up a double-play grounder by Raul Ibanez to end that inning.
"You can't say enough about the defence of Anthony Gose in left field," Blue Jays manager John Farrell said. "Not only the double play where he goes up against the wall and doubles up the runner at first.
"But holding Martin to a single rather than letting that ball get in the corner for a double, keeps another double play in order."
Morrow (9-7) held the Yankees to four hits and three walks while striking out three to gain his first victory since Aug. 31. He had two losses in his previous four starts.
"He made a very good adjustment coming out of his last start in Tampa Bay where they laid off his slider off the plate where he threw some quality ones, but they didn't expand the strike zone," Farrell said. "He tightened up his slider tonight to force the Yankees to respect that pitch. He used his change-up to both righties and lefties."
Right-hander Ivan Nova (12-8) allowed six hits, two walks and four runs in 4 2/3 innings.
"He wasn't as sharp as he was a couple of outings ago," Girardi said. "He just hasn't had the command, that's the bottom line."
Blue Jays shortstop Yunel Escobar received a few boos from the crowd in his first at-bat in the first but there was little crowd reaction to him after that.
It was his first appearance in Toronto since the club suspended him for three games last week for writing a homophobic slur on his eyeblack for a game at Rogers Centre against Boston on Sept. 15. Escobar lined out to the shortstop.
"In the three years he has spent in Toronto the fans have been great to him," Escobar said through interpreter Luis Rivera, a Blue Jays coach. "They know how hard he works and he gives everything on the field. Again, he said made a mistake and he's sorry for it."
The eyeblack incident had created some backlash among Toronto baseball fans before Thursday's game, however.
An online petition asking the Blue Jays to create a You Can Play video encouraging the acceptance of homosexuals in sports has been started by openly-gay Blue Jays fan Christopher Papps.
The Blue Jays (69-87) took a two-run lead in the third on Lawrie's 10th homer of the season that followed a one-out walk by Gose.
Gose led off the home fifth with a single. Colby Rasmus bunted for a single with one out and Encarnacion scored both runners with a double to right.
The Blue Jays tacked on a run in the seventh against Derek Lowe with Lawrie scoring from third on Encarnacion's bouncer to shortstop. Lawrie and Rasmus singled with one and advanced to second and third on a wild pitch.
Arencibia hit his 18th homer of the season in the eighth against reliever David Aardsma.
Notes: Attendance at Rogers Centre was 23,060. ...Escobar met for about 45 minutes Thursday afternoon with Patrick Burke, founder of the You Can Play project established to help eliminate the homophobic culture sometimes found in sports. "I was very happy with how today went," Burke said before the game. "I wasn't sure what to expect going in between the language issues and the entire incident, how it all went down. ... I thought Yunel was very receptive to what we were talking about." ....Blue Jays rookie infielder Adeiny Hechavarria who is on a nine-game hitting streak did not start Thursday's game . ..The Blue Jays have lost 12 of their past 17 series. ...Chad Jenkins (0-2, 4.24 ERA) will make his second major-league start Friday against New York's Hiroki Kuroda (14-11, 3.34 ERA). Jenkins had made 10 relief appearances since being called up from Class-AA New Hampshire.