Daulton Varsho had two home runs among his four extra base hits, and Ernie Clement and George Springer also both homered as Toronto reached double figures in hits (15) and runs for the second straight game.
The Blue Jays had three home runs among their 14 hits Saturday in a 10-1 victory. They have as many home runs (eight) as strikeouts (seven) through two games.
Varsho went 4 for 5 with two doubles, scored four runs and drove in four. Guerrero went 3 for 5 and scored twice.
Cody Bellinger homered and drove in three runs and Ben Rice had two hits and two RBIs in a five-run seventh but Toronto won for the eighth time in nine home meetings with New York. The Blue Jays went 2-4 in six games at Yankee Stadium, where the series shifts for Game 3 on Tuesday night.
Yesavage (1-0) was selected by Toronto with the No. 20 pick last year in the amateur draft. The 22-year-old right-hander rose through four minor league levels this season before joining the Blue Jays and going 1-0 in three September starts.
Yesavage needed fewer than four innings to beat Toronto's previous record for postseason strikeouts, eight, held by Dave Steib, David Price (twice) and Juan Guzman
Known for his elite split-finger fastball, Yesavage set a Blue Jays record by striking out nine Rays batters in his Sept. 15 debut. Eight of his 11 strikeouts Sunday came on the splitter. The other three came on fastballs that reached 96 mph.
Yesavage opened the game by striking out Trent Grisham on a splitter. He walked Aaron Judge on four pitches, then fanned Bellinger and Rice to start a streak of 12 straight outs that ended when Jazz Chisholm Jr. reached on Guerrero's fielding error in the fifth.
Yesavage responded by getting Ryan McMahon to pop up and fanning Anthony Volpe for his 11th strikeout.
Yesavage struck out six straight over the third and fourth innings as Volpe, Austin Wells, Grisham, Judge, Bellinger and Rice were retired.
Left-hander Justin Bruihl came on to face Grisham after Yesavage threw 78 pitches, 48 for strikes. Manager John Schneider was booed as he came out to remove Yesavage with Toronto leading 12-0. The crowd of 44,7564 then roared until Yesavage came out for a curtain call, lifting his arms over his head at the top of the dugout steps.
Bruihl retired Grisham on a grounder before Judge reached on an infield single for New York's first hit. Bellinger followed with a homer.
Yankees left-hander Max Fried (0-1) allowed seven runs and eight hits in 3-plus innings. He gave up seven runs in 33 1/3 innings in five September starts.