Brooks intercepted a pass and forced a fumble and Phillips grabbed a fumble and ran 38 yards for a score in the Bucs' third victory in four games.
Matt Bryant kicked three field goals, including a 24-yarder that sent the Bucs ahead with under 3 minutes to play.
Greg Jennings caught two touchdown passes for Green Bay (2-2).
Packers' quarterback Aaron Rodgers passed for 165 yards and was picked off three times. Rodgers left the contest in the fourth quarter with a shoulder injury.