DeJesus supplied a pair of RBI doubles, Loney added a two-run double and Matt Joyce socked a solo homer for the Rays, who maintained their grip on the first American League wild-card spot with a fifth straight triumph.
Matt Moore (16-4) overcame six walks to record five shutout innings en route to the victory, allowing three hits while striking out four.
Jake Odorizzi finished up with three scoreless innings for his first career save as the Rays notched a club-record 16th shutout on the season.
Hiroki Kuroda (11-13) was roughed up for five runs on five hits in a 5 2/3-inning start for the Yanks, who are one loss or one Cleveland victory away from missing the playoffs for the first time since 2008.
Celebrity Families of 2014 [PHOTOS]