Kaepernick completed 27-of-39 passes for the 49ers (1-0), who posted a victory in their first game since falling to Baltimore 34-31 in Super Bowl XLVII.
Frank Gore put San Francisco ahead to stay at 31-28 with a 1-yard touchdown run with 5:47 left in the game.
Green Bay (0-1) got a 333-yard, three-touchdown passing performance from Aaron Rodgers but it wasn't enough for the NFC North champions.
Jordy Nelson and Randall Cobb combined for 238 yards on 14 catches for the Packers.
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