The Braves took two of three games in an interleague matchup of division leaders. They've won four of five overall and 11 of 12 at home to improve to 21-7 at Turner Field.
Tampa Bay's two-game slide dropped the Rays to 9-13 since May 23.
Hudson (7-2) lowered his ERA nine points to 2.34 after allowing four hits, one run and four walks with five strikeouts. The right-hander improved to 113-21 in his career when pitching at least seven innings.
Glaus, whose 53 RBI include 27 with two outs, gave the Braves their first lead at 3-1 with a two-run double in the sixth.
Atlanta improved to 9-0-3 in its last 12 series. The Braves were 13-18 after losing May 9 at Philadelphia, but are 26-10 since.
In 11 career starts against Tampa Bay, Hudson is 7-1 with a 2.71 ERA.