The Saints drove 31 yards on the opening possession before Derek Carr, who was being pressured, threw a ball up for grabs in double coverage. Bryan Cook intercepted it at the Kansas City 22.
Ten plays and 78 yards later, the Chiefs took a 7-0 lead.
Kareem Hunt scored on a 5-yard touchdown run with 6:34 remaining in the first quarter. The running back had 23 yards on five carries on the drive.
Patrick Mahomes went 4-for-4 for 46 yards, with Travis Kelce catching three passes for 31 yards.