Hyun Jin Ryu (13-8) pitched six effective innings as the Blue Jays won for the eighth time in nine games. Toronto also improved to 5-2 in the Bronx this year.
Guerrero hit his 40th homer on Jameson Taillon's 13th pitch, a full-count curveball that landed a few rows into the seats in right. The slugger and his Hall of Fame father joined Cecil and Prince Fielder as the second father-son duo to hit 40 homers.
Guerrero finished with three hits, extending his hitting streak to a career-high 14 games.
Guerrero Sr. hit 449 homers in his 16-year career. His career high was 44 for the 2000 Montreal Expos when Toronto's slugging first baseman was 1 year old.
''I have front-row seats to watch this whole season,'' said Toronto manager Charlie Montoyo, a teammate of Guerrero Sr. in 1996 with Double-A Harrisburg. ''What he's done, that's not easy to do. This guy he's going to be one of the best players in baseball. Actually, he already is and it's been fun to watch somebody that young be that good at the plate.''
The 22-year-old Guerrero also became the youngest player in Toronto history to hit 40 homers, well ahead of Jesse Barfield, Tony Batista and Shawn Green, who were all 26 years old when they hit 40 homers for the first time.
Guerrero also became the 10th player in MLB history with 40 homers in his age-22 season. The last was Atlanta's Ronald Acuna Jr. in 2019.
''That's amazing,'' Semien said. ''I knew when we took BP, it was a good day to hit to right field. He didn't hit on the field but I mentioned that to him. He's so good he did it in his first at-bat. It's something special.''
Semien hit a solo drive in the first and his fifth career grand slam in the ninth. He has five homers in his last five games and a career-high 37 on the year.
Teoscar Hernandez also went deep in the ninth for the Blue Jays.
Ryu held the Yankees to three singles after losing his previous two starts. He struck out six, including Joey Gallo three times, and walked none.
Ryu was lifted after 80 pitches. He said he felt some tightness in his right forearm when he threw a slider. He did not seem to think it would prevent him from making his next start.
''I felt really good with all my pitches today and I feel like it's one of those games that I felt my best,'' Ryu said through a translator.
Ryu also got some help from a slimmed-down Guerrero at first base. Guerrero, who lost 42 pounds in the offseason, made two nice stretches to get a throw from shortstop Bo Bichette in the fifth and a toss from Semien on a double play in the sixth.
Coming off a pair of one-run losses to the lowly Orioles, the Yankees lost for the seventh time in nine games following their first 13-game winning streak since 1961. The Yankees began the day with a half-game lead over Boston for the AL's first wild card.
''It's a concern,'' Yankees manager Aaron Boone said. ''These are big-time games right now. These are important games. I want us to play well. We need to dig ourselves out of this little funk we've been in for a week.''
New York struck out 10 times and had one at-bat with runners in scoring position. Its 2-3-4 hitters of Gallo, Aaron Judge and Giancarlo Stanton finished a combined 0 for 11 with seven strikeouts.
Taillon (8-6) allowed three runs and three hits in seven innings. He lost his second straight start following a 15-start unbeaten stretch.
Trevor Richards and Tim Mayza pitched a scoreless inning apiece. Adam Cimber finished the five-hitter for Toronto's AL-best 14th shutout.
The Yankees committed three errors but Toronto did not capitalize on any of them.
Shortstop Gleyber Torres bobbled a grounder in the second by Gurriel, who was thrown out trying to steal second base later in the inning.
Gio Urshela also committed a pair of miscues at third in his first game back from a brief absence with a hand injury.
Danny Jansen's soft liner deflected off Urshela's glove in the second, and he also bobbled a grounder by Guerrero. The Yankees ended the third when Brett Gardner made a diving catch in center and easily doubled off Guerrero.
Blue Jays: DH George Springer fouled a ball off his knee in the eighth. He was checked out, stayed in but gingerly walked back to the dugout after striking out. He was replaced by Jake Lamb in the ninth. Montoyo said Springer has a contusion and is day to day.
RHP Gerrit Cole (14-6, 2.73 ERA), who struck out 15 in seven innings Wednesday against the Angels, starts for New York against Toronto LHP Steven Matz (10-7, 3.80 ERA). Matz pitched 6 2/3 innings of one-run ball on May 25 in New York.
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