Overbay drove in two runs, and Edwin Encarnacion and Joe Inglett also drove in runs for the Blue Jays, who played an inspired game about 30 minutes after learning that teammate Alex Rios had been claimed off waivers by the Chicago White Sox.
The Blue Jays' bullpen gave up four hits over 5 2/3 scoreless innings, helping Toronto win for only the third time in 10 tries against the Yankees this season.
Jason Frasor worked the ninth inning for his fifth save.
Derek Jeter hit a home run on the third pitch from Rzepczynski, and Robinson Cano and Jerry Hairston connected for consecutive home runs in the fourth inning for the Yankees.
Yankees starter Sergio Mitre (1-1) gave up five runs -- three earned -- and six hits in five innings.