Teoscar Hernandez and Russell Martin also homered for the Blue Jays (72-82) in the opener of a three-game series.
Aaron Judge homered for the Yankees (85-68).
Estrada (10-8) held the Yankees to one run on three hits with three walks and four strikeouts over seven innings in his first start since signing a one-year, $13-million contract extension.
Yankees starter Masahiro Tanaka (12-12) allowed eight runs (seven earned), six hits that included three home runs, and three walks in 5 2/3 innings. He struck out six.
Goins hit his second grand slam of his career -- both this season -- to give the Blue Jays an 8-1 lead. Goins has eight home runs this season and 59 RBIs.
Tommy Kahnle replaced Tanaka and struck out Hernandez to end the inning.
Toronto's Matt Dermody retired the first two batters in the top of the eighth before Tom Koehler took over to face Judge, who walked before Gary Sanchez ended the inning by grounding out to third.
Carlos Ramirez pitched a perfect ninth for Toronto.
Judge hammered his 46th homer of the season to left in the first inning.
The Blue Jays tied the game in the bottom of the first with an unearned run.
Hernandez led off with a single. He went to third when second baseman Starlin Castro missed the catch from third baseman Todd Frazier in the attempted force play at second on a grounder by Josh Donaldson.
After Justin Smoak struck out, Hernandez scored when Bautista grounded out on a chopper to third.
The Yankees could not take advantage of a leadoff double by Todd Frazier. He ended the inning when Blue Jays shortstop Goins faked a throw to the pitcher and tagged him after he had stepped off the bag. Goins had just taken the throw from Bautista, who had made the catch in deep right on a drive by Jacoby Ellsbury.
Hernandez hit his third homer of the season with one out in the bottom of the third to give the Blue Jays a 2-1 lead.
The Blue Jays took a 4-1 lead in the fourth on Martin's 13th homer of the season that also scored Bautista, who had started the inning with a walk.
NOTES: Blue Jays c Russell Martin's home run in the fourth was first since Aug. 4. He went on the disabled list Aug. 12 with a left oblique strain and missed 30 games. The homer was his third of the season with a runner on base. ... Blue Jays C Miguel Montero, used at DH Friday, singled in the eighth to end a 0-for-15 slump. ... Yankees OF Brett Gardner, who is on an 11-game hit streak, did not play. He is 6-for-39 (.154) against Toronto RHP Marco Estrada, who started Friday. ... Blue Jays RHP Joe Biagini (3-11, 5.33 ERA) opposes Yankees RHP Sonny Gray (9-11, 3.38) on Saturday.