Aaron Rodgers threw two second-half touchdown passes and led an overtime drive that resulted in Mason Crosby's 31-yard field goal as time expired, lifting the Packers to a 27-24 victory on Sunday.
The dramatic finish came after Rodgers went 4 of 11 for 44 yards for an 11.2 passer rating in a first-half performance that included New England's Jack Jones scoring on a 40-yard interception return, lifting the Patriots to a 10-7 halftime lead.
Hoyer led New England to Nick Folk's 37-yard field goal on the game's opening drive, but he got sacked by Rashan Gary on the team's next series and departed.
Zappe and the Patriots (1-3) still played well enough to force overtime, but Rodgers continued his recent home mastery of AFC teams. The Packers (3-1) are 18-1 in the last 19 home games Rodgers has started against AFC foes.
Aaron Jones rushed for 110 yards to lead Green Bay's 199-yard attack on the ground. Allen Lazard had six catches for 116 yards.
Zappe gave New England a 17-10 lead in the third quarter with a 25-yard touchdown pass to DeVante Parker. The ball appeared to get snapped after the play clock had expired on Parker's touchdown, but no penalty was called.
After Crosby's 38-yard field goal late in the third, New England regained the lead on Damien Harris' 5-yard touchdown run with 11:14 left. Harris rushed for 86 yards on 18 carries, while Rhamondre Stevenson ran 14 times for 66 yards.