Acquired from Detroit on Sunday as part of a four-player trade, Cardona singled twice, was hit by a pitch and slugged a three-run homer off reliever Valerio de los Santos in the sixth inning.
Phil Nevin also was 3-for-3 and hit his fifth spring homer, a solo shot off starter Jamey Wright in the third to extend the Padres' lead to 6-0.
Bobby Jones went six innings for San Diego and gave up three runs and seven hits with four walks and three strikeouts.
Jeremy Fikac and David Lundquist combined for three hitless innings.
Wright surrendered six runs, seven hits and five walks in 3 2/3 innings for the Brewers, who had just seven singles and got two RBI from Matt Stairs.