Wes Helms opened the sixth with a single and Eddie Perez reached base when Twins third baseman Michael Cuddyer bobbled his ground ball. After Royce Clayton bunted into a fielder's choice, Kieschnick singled up the middle to plate Perez for the go-ahead run.
Kieschnick struck out two, walked one and did not yield a hit en route to his third spring victory. Curtis Leskanic tossed a perfect ninth for the save.
Brewers starter Jamey Wright allowed four runs -- two earned -- and five hits in four innings. He also drove in a run.
Eric Young went two for three with an RBI and one run scored and Jeffrey Hammonds drove in a run for Milwaukee.
Pinch-hitter Todd Sears drove in two runs and Cuddyer and Doug Mientkiewicz each drove in a run for the Twins.
Rick Reed started for Minnesota, giving up two runs and four hits in three innings. After Joe Mays surrendered two runs and four hits in two innings, Tony Fiore took the loss.