Gross's RBI double drew Tampa Bay within 3-2 with one out in the seventh. Carlos Pena and Evan Longoria had one RBI apiece, while Pena, Ben Zobrist and Carl Crawford all had two hits for the Rays, who went 6-0 against the Royals this season.
The winner was reliever Grant Balfour (4-1).
Closer J.P. Howell earned his 20th save with a 1-2-3 ninth.
Alberto Callaspo led Kansas City with three hits and two RBI. David DeJesus had one RBI and Billy Butler had four of the 11 hits for the Royals, whose losing streak grew to six straight games despite an early 3-0 lead. They have lost 11 of their last 14 games against the Rays.
The losing pitcher was Jamey Wright (0-3). He surrendered two runs in relief of Royals' starter Luke Hochevar, who went 6 1/3 innings, allowing two runs on seven hits with no walks and nine strikeouts.