Erick Aybar had two hits and one RBI, one run scored on a fielding error by Brendan Harris, while Hillenbrand, Matthews, and Mike Napoli all had two hits for the Angels, who have won four of their last five games.
Winner John Lackey (3-2) scattered an earned run and seven hits over six innings with two walks and seven strikeouts.
Delmon Young had three hits of the eight hits and one RBI for the Devil Rays, who have split their last four games.
Three Tampa Bay errors led to six unearned runs.
Loser Edwin Jackson (0-3) was charged with eight hits and six runs -- three earned -- in six innings.