The Phillies bullpen combined to toss four scoreless innings, surrendering just three hits.
The Brewers knocked Hector Neris around to open the ninth inning with a pair of singles, but he was able to close out the frame unscathed.
Hellickson had thrown 85 pitches before being lifted for Cameron Perkins as a pinch-hitter in the sixth.
Odubel Herrera finished with a pair of doubles in the winning effort.
Aaron Altherr was out of the lineup again, nursing a hamstring issue that appears serious enough for a trip to the disabled list.
Brewers starter Matt Garza lasted five innings, surrendering just one run but issuing three walks. Maikel Franco, Andrew Knapp, and Tommy Joseph pieced together consecutive singles chasing reliever Rob Scahill to open the sixth, Williams then deposited Tyler Webb's first pitch over the fence in center to give the Phillies a three-run lead.
Despite the outcome, the Phillies struggles with runners in scoring position continued - finishing just 3-for-13 while also leaving eight runners on base. The Phillies entered Sunday hitting .233 with runners in scoring position, fourth worst in the majors.
The Phillies will travel to Miami and open a three-game set with the Marlins on Monday.
_______________________________
Follow Patrick on Twitter: @PGordonPBR
