Tate, who caught a TD pass in the first quarter, was credited with the score after the officials ruled he had caught a 24-yard Hail Mary pass in the end zone from Russell Wilson that appeared to have been intercepted by M.D. Jennings but was instead ruled a catch.
The ruling was made by the officials as Tate and Jennings wrestled for the ball. The call was upheld by the video replay.
"I've never seen anything like that in all my years of football," Packers Coach Mike McCarthy said afterward. "It was the most unusual football game I've ever been a part of."
Green Bay (1-2) had taken the lead with 6:02 to play in the game on a 1-yard run by Cedric Benson.
Mason Crosby kicked two third-quarter field goals for the Packers and Aaron Rogers was 26-of-39 for 233 yards passing.
Wilson was 10-for-21 for 130 yards passing for the Seahawks (2-1). Marshawn Lynch carried 25 times for 96 yards.
Despite the theatrics on the final play, the game was largely defensive and closely called by the replacement officiating crew. Green Bay had a modest 268 net yards of offense to Seattle's 238. Seattle was called for 14 penalties totaling 118 yards and Green Bay had 10 flags for 127 yards.