Rodriguez's 537th home run moved him past Mantle, a beloved Yankees great, and into sole possession of 13th place. A-Rod drove a 3-2 pitch from left-hander Brian Tallet off the left-field foul pole to begin the fourth inning, his 19th of the season.
It was Rodriguez's 192nd home run with the Yankees, tying Tino Martinez for 15th place on the franchise list.
The three-time AL MVP has 47 career home runs against Toronto, his second-highest total against any opponent. He has hit 58 homers against the Los Angeles Angels.
A-Rod's milestone shot came three innings after Jeter led off the game with a drive to right, his fifth of the year. It was the 18th time Jeter has led off a game with a home run.
New York right-hander Darrell Rasner gave up four runs in the first but shut out the Blue Jays over the next four innings to win for just the second time in nine outings. He snapped a three-start losing streak.
Rasner (5-7) allowed three earned runs and seven hits. He walked one and matched a season high with six strikeouts.
Edwar Ramirez, Jose Veras and Kyle Farnsworth each worked a hitless inning before LaTroy Hawkins wrapped it up with a 1-2-3 ninth.
Toronto's Jesse Litsch (8-6) gave up eight runs - three earned - and seven hits in 2 2-3 innings. The right-hander, who began the season 7-1, has won just once in his past eight outings.
Trailing 1-0 on Jeter's home run, Toronto put Rasner in an early hole by sending eight batters to the plate in the first. Marco Scutaro hit an RBI single and Adam Lind had a three-run triple.
New York jumped back in front in the second, loading the bases with a walk, a single and a hit batter. Gardner hit a run-scoring single and Jeter drove in a run when Scutaro bobbled a potential double-play grounder to second. One out later, Rodriguez hit a two-run single.
The Yankees chased Litsch with a three-run third. Robinson Cano reached on an error by shortstop John McDonald, Melky Cabrera singled and both runners advanced on a grounder before Gardner hit a two-run single and scored on Jeter's single.
The crowd of 44,363 was Toronto's biggest since opening day, surpassing Friday's crowd of 43,078.
