Brees broke his own record of ten 300-yard-plus games in a season with Sunday's performance, in which he hooked up with Darren Sproles five times for 79 yards and a touchdown.
Jimmy Graham chipped in with seven receptions, 70 yards and another score.
New Orleans will seek to wrap up the NFC South title with a win over the Atlanta Falcons next week.
Christian Ponder struck for a pair of TD passes for the Vikings (2-12), who lost a sixth consecutive game for the first time since 1984.
2014: The Year in Music [PHOTOS]