Matt Chapman homered with two outs in the seventh to spoil the shutout bid for Paddack (1-3), who had six strikeouts without a walk in his first win since last June 10.
Byron Buxton, who reached base three times, hit the first pitch from Giants starter Jordan Hicks (1-4) off the wall in right-center field for a triple and scored on a single by Trevor Larnach.
The Twins (19-20) matched their longest winning streak since six straight from last June 12-18.
Buxton, who wasn't credited with an RBI on his one-out single because Giants left fielder Heliot Ramos bobbled the scoop for an error, got Harrison Bader home for a 3-0 lead in the fifth.
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Logan Webb starts for the Giants on Saturday night, when Joe Ryan will pitch for the Twins. Ryan's start was pushed back two days by an illness.
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