New Orleans took the opening kickoff and went 84 yards in 18 plays, bleeding 6:31 off the clock to take a 7-0 lead.
Alvin Kamara had only three carries, but he gained 32 yards with 27 coming on one carry.
Hill went 4-for-4 for 38 yards.
The Saints did not face a third down in scoring their first opening drive touchdown of the season. They had not scored a first quarter touchdown since Week 8.