Hoyer connected with Britt Davis on a 3-yard scoring toss that capped a 97-yard scoring drive.
Hoyer completed 8-of-15 passes for 45 yards in the contest.
Tom Brady opened the game for the Patriots and completed 4-of-7 passes for 30 yards. He was also sacked and fumbled the ball.
Patriots tight end Rob Gronkowski came back from off-season ankle surgery and caught two passes for 20 yards.
The Saints got their scoring from Garret Hartley, who kicked a 27-yard field goal, and John Kasay, who booted one of 46 yards. Kasay had a chance to give the Saints the lead with 3:07 left in the game but his 41-yard kick missed.