Kaepernick's 5-yard scoring strike to Quinton Patton in the first quarter made it 10-0 for San Francisco, which never trailed in the contest.
Phil Dawson converted both his field goal tries in the victory.
Christian Ponder completed 17-of-23 pass attempts for 116 yards and a pair of touchdowns but also lost a fumble and tossed an interception for the Vikings, who are winless in the pre-season.
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