Crawford and Andy Sheets belted three-run shots off Royals starter Shawn Sedlacek (2-3) and Aubrey Huff and Steve Cox had solo homers as the Devil Rays registered their highest run total of the season.
Victor Zambrano (5-4) picked up his first career win as a starter despite yielding five runs and seven hits in five innings.
Wilson Alvarez allowed a run and two hits in the final four innings as the veteran recorded his second career save and first since Opening Day of the 1992 season as a member of the Chicago White Sox.
Raul Ibanez homered and had three RBI for the Royals, who lost for the seventh time in 10 games.
2014: The Year in Music [PHOTOS]