Hancock, 29, was killed in an auto accident Sunday and St. Louis canceled its Sunday night game against the Chicago Cubs.
Suppan (4-2) scattered eight hits and one run with one walk and five strikeouts. His fourth victory gives the Brewers two four-game winners in April for the first time in franchise history. Chris Capuano also has four wins.
Prince Fielder hit his sixth home run for Milwaukee. Kevin Mench had a pair of hits, scored twice and drove in two runs, and Johnny Estrada drove in two runs for the Brewers, who are in first place in the National League Central.
Swim Week Miami Beach 2014 [PHOTOS]