Hellickson (9-7) won his second straight start after breaking a personal four-game losing streak, allowing five hits, walking only one and striking out seven. The rookie right-hander was making his first career start against the Yankees.
Jake McGee tossed a scoreless eighth and Joel Peralta earned his first save of the season and the third of his career with a 1-2-3 ninth for the Rays, who evened their four-game series with New York at one win apiece.
The Rays took the lead with a pair of runs in the seventh, scoring on Boone Logan's fielding error and a sacrifice fly by Johnny Damon.
Bartolo Colon (6-6) was tagged with the loss, yielding two earned runs on five hits before exiting after 6 1/3 innings.
Robinson Cano cracked a two-run homer for the Yanks, who remained 1 1/2 games behind first-place Boston in the AL East.
Notable deaths of 2014 [PHOTOS]