Suzuki said he felt ashamed after failing to catch Edwin Encarnacion's fly ball to deep right in the fifth inning, a play that keyed a three-run inning for Toronto.
"If I could have just gone straight home from right field, I would have," Suzuki said through a translator. "I was that embarrassed."
It was just the third error of the year for Suzuki, who has never had more than five miscues in any of his 13 major league seasons.
"Something you're not going to see very often," Yankees manager Joe Girardi said. "It just looked like he jumped for it and maybe he didn't have to. Maybe he was closer to the wall than he thought."
Alex Rodriguez hit his 650th home run, a leadoff drive in the fifth, but the Yankees lost for the ninth time in 13 road games this month. Rodriguez is 10 homers away from tying Willie Mays for fourth on the career list, which would secure a $6 million bonus for the third baseman.
Derek Jeter went hitless in his return to New York's lineup. Jeter, who started at shortstop and batted second, finished 0 for 3 with a walk, grounding into a double play in the third.
"He looked fine," Girardi said. "Everything looked OK to me."
Reyes walked and scored in the third, and doubled and scored in Toronto's three-run fifth as the Blue Jays beat the Yankees for the second time in 14 meetings this season. Toronto had lost 10 straight to its division rival since an 8-4 home win on April 21.
"Everything fell in line tonight," Blue Jays manager John Gibbons said.
Dickey (10-12) allowed two runs, one earned, and six hits in 6 1/3 innings to win for the first time since Aug. 5 at Seattle. The knuckleballer was 0-1 with a 4.50 ERA in his three previous starts.
"Unfortunately for us, we couldn't figure out the knuckleball," Jeter said.
It was Dickey's first victory over the Yankees since May 21, 2011, when he pitched for the New York Mets.
"He gave us just what we needed," Gibbons said.
Rodriguez's home run was the 29th allowed by Dickey this season, second only to Oakland's A.J. Griffin. Dickey has given up 20 homers in 14 home starts.
New York right-hander Phil Hughes (4-13) allowed five runs, four earned, and seven hits in 4 2/3 innings. He is 0-6 with a 5.84 ERA in his last nine starts.
"I left a lot of sliders over the middle of the plate," Hughes said. "It didn't really seem like it had the bite that it did in the last couple (of starts)."
Girardi said Suzuki's error was tough on Hughes, and insisted that the righty's spot in the rotation is safe.
"Right now he's in our rotation and we haven't talked about taking him out," Girardi said.
Even so, Girardi acknowledged that the Yankees, who are pushing for an AL wild card berth, are "thinking all the time" about their starters.
New York scratched out a run in the first when Brett Gardner singled, went to second on a passed ball, took third on Jeter's grounder, and scored when Dickey couldn't handle Robinson Cano's comebacker.
The Blue Jays tied it in the second on an RBI single by Kevin Pillar, and then took the lead on Encarnacion's RBI single in the third.
Rodriguez connected in the fifth, but Toronto responded with three in the bottom half, making the most of Suzuki's drop.
Reyes hit a one-out double, Ryan Goins singled, and Reyes scored when Suzuki couldn't handle Encarnacion's fly to deep right, with the ball hitting off the heel of his glove.
"You never see Ichiro drop a pop-up but it worked out good for us," Reyes said.
Adam Lind followed with an RBI double, and Brett Lawrie was intentionally walked to load the bases for Moises Sierra, who chased Hughes with a sacrifice fly. David Huff came on and fanned Josh Thole on three pitches.
Rodriguez has 35 home runs at Rogers Centre, the most by any Toronto opponent. ... Blue Jays OF Colby Rasmus (strained left oblique) is still sore and was unable to resume baseball activities as previously scheduled, Gibbons said. Rasmus has been out since Aug. 12. ... Toronto reinstated Loup from the paternity list and designated RHP Chien-Ming Wang for assignment. ... Blue Jays Triple-A C Sean Ochinko was suspended 50 games after testing positive for amphetamines. ... Musician Paul Simon attended the game.