Dickey (10-1) won his ninth straight decision and became the first pitcher in the majors this year to reach 10 victories. He surrendered a two-out, infield single to B.J. Upton in the first inning and no other Tampa Bay batter reached base after that until Elliot Johnson was safe at first on a throwing error by third baseman David Wright leading off the ninth.
A pair of passed balls charged to Mike Nickeas put Johnson on third and he scored the Rays' only run on a groundout.
The one-hitter turned out to be the second complete game of the year for Wright and the sixth of his 10-year career. He struck out 12 and did not allow a walk.
David Price (8-4) suffered the loss while giving up seven runs on nine hits in five innings.