Robinson Cano hit a two-out single in the first, his first hit since Friday, and Alfonso Soriano followed with a double. Lyle Overbay walked to load the bases, but Dickey fanned Mark Reynolds for the final out.
New York stranded two more runners in the second when Stewart walked with two outs and Granderson singled him to second. Rodriguez followed with a grounder to short.
"It was unfortunate both of those rallies started with two outs," Girardi said. "We had some opportunities and then after that we didn't really do too much."
Dickey, who threw 51 pitches in the first and second innings, retired 15 of the next 16 Yankees and erased his only mistake, Reynolds' leadoff single in the fourth, on a double play.
Pinch-hitter Adam Lind hit a two-out single off David Robertson in the eighth and tried to score on pinch-hitter Anthony Gose's double, but was thrown out at the plate on a relay from shortstop Brendan Ryan.
NOTES: Toronto was eliminated from wild card contention when Texas won at Tampa Bay. ... Blue Jays 1B Edwin Encarnacion (left wrist) and LHP Brett Cecil (left elbow) will miss the remainder of the season. Encarnacion is scheduled to undergo surgery. ... Yankees LHP Boone Logan has been diagnosed with bone spurs in his elbow, but will try to pitch through the pain. ... New York C Austin Romine (concussion) was scratched from the starting lineup and replaced by Stewart. ... Janssen celebrated his 32nd birthday.