Davis hit a home run in each game of the season-opening series and was 7-for-11 with 11 runs batted in.
Davis opened the scoring with a two-run drive to center in the second inning and broke a 2-2 tie with a two-run double into the gap in left-center in the sixth.
Both of Davis' hits came off Roberto Hernandez (0-1), who struck out seven but also gave up six hits and walked two in 6 2/3 innings.
J.J. Hardy added a two-run home run -- his first of the year -- in the eighth for the Orioles.
Tampa Bay managed five hits and two runs off Miguel Gonzalez (1-0), who struck out four and walked two. Jim Johnson picked up his second save.