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.