Minnesota has lost 10 of its last 13 games.
Kinney (6-6) blanked his former team until he gave up an RBI double to Torii Hunter in the sixth. The righthander walked one, struck out four and lowered his ERA from 4.58 to 4.26.
Twins manager Ron Gardenhire thought his team would show "a little more fire" in Thursday's 5-1 loss to the Chicago White Sox. But Minnesota continued to look flat in the opener of this series.
John Vander Wal hit a two-run homer in the fifth before Richie Sexson added a three-run shot, his 22nd, in the seventh to give Milwaukee a 9-1 cushion.