TORONTO -- Aaron Hicks tied his career high for RBIs in a game with one swing of the bat in the first inning.
"It's awesome," the Yankees' center fielder said. "You always want to have big games, and I was able to do that."
Sabathia (6-2) allowed five hits and two runs while striking out seven in 6 1/3 innings.
He finished the start with 2,779 career strikeouts to pass Frank Tanana (2,773) for fourth on the all-time list for left-handed pitchers.
"The cutter was really good again tonight," Yankees manager Joe Girardi said. "His sinker was pretty good and his changeup and slider were good, too. He had everything tonight. It's a very dangerous lineup; he controlled it."
Sabathia appreciated the run support.
"It's fun to watch (Hicks) go out and do his thing," he said. "If we get (Sanchez) hot, this lineup is going to be tough to deal with."
Kendrys Morales and Ezequiel Carrera homered for the Blue Jays (26-28), who had just completed an 18-10 May.
Blue Jays starter Marco Estrada (4-3) allowed nine hits, including two home runs, plus two walks and seven runs in 3 2/3 innings.
"I thought it just wasn't his night; that's rare," Blue Jays manager John Gibbons said. "I can't remember the last time we saw an outing like that. No use abusing him; he's done too much for us."
Leonel Campos replaced Estrada and pitched well for three innings. He allowed only a walk until second baseman Darwin Barney's two-out error on a grounder by Didi Gregorius in the seventh set up two unearned runs. Hicks followed with an RBI double and Chase Headley had an RBI single that gave New York a 9-0 lead.
"I didn't make any good pitches today. It just wasn't there," Estrada said. "I got more upset about having the bullpen pick up all those innings. It's my job to go deep into the game regardless of how any runs I give up. They did a good job. Campos had a really good outing. I'm happy for him."
Morales led off the bottom of the seventh with his 11th homer of the season. Sabathia struck out Justin Smoak and was replaced by Chad Green.
Carrera led off the bottom of the eighth with his fourth homer of the season.
Holliday and Gregorius singled in the ninth against J.P. Howell, and Hicks drove them home with a double. Headley greeted Ryan Tepera with an RBI single.
The Yankees scored four runs in the first. Brett Gardner led off with a double, advanced to third on a line out to center by Sanchez and scored on a single by Aaron Judge. A single by Holliday moved Judge to third, and Starlin Castro walked to load the bases. Gregorius struck out, but Hicks cleared the bases with a double to right on a changeup.
"I thought the real big hit was the hit that Hicksy got with two outs," Girardi said. "We made (Estrada) work really hard. He threw a lot of pitches the first inning, threw a bunch of pitches in the second inning, and it made a difference. We never really let him settle in tonight.
"It's probably one of the bigger nights (Hicks) has had in his career. Great way to start four days here."
Sanchez homered with two outs in the second to increase New York's lead to 5-0.
The Yankees' catcher hit his second homer of the game and sixth of the season, with one out in the fourth inning after Gardner singled for a 7-0 lead. Both Sanchez's homers against Estrada were on changeups.
After a single by Holliday, Leonel Campos replaced Estrada.
Bad location on the changeup was a key to Estrada's troubles.
"Sanchez hit two (changeups) today off of me," Estrada said. "It's basically what he did to me last time at their place. I missed two changeups and he crushed those. I've got to stop missing changes. When they're down, I get swings and misses; when they're up like that, they get hit a long way. That's basically what happened."
NOTES: Toronto designated RHP Mike Bolsinger for assignment and recalled RHP Leonel Campos from Triple-A Buffalo. Bolsinger was 0-2 with a 5.61 ERA in four starts with Toronto. Campos was optioned back to Buffalo after the game. ... Yankees SS Didi Gregorius was back in the lineup after being given the day off Wednesday at Baltimore after being hit on the hand by a pitch on Tuesday. ... Toronto C Russell Martin and 2B Devon Travis did not play Thursday to give them a rest. ... Yankees RHP Michael Pineda (6-2, 3.32 ERA) faces Blue Jays LHP Francisco Liriano (2-2, 6.35 ERA) on Friday. It will be Liriano's first start since May 10 because he has been out with a sore shoulder.