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.
2014: The Year in Music [PHOTOS]