Brees went 31-of-35 through the air with no interceptions. He hooked up on two scoring passes each to Marques Colston (seven catches, 98 yards) and Jimmy Graham as the Saints rolled up 557 yards of total offense.
Mark Ingram gained 91 yards on 14 carries for New Orleans, which smashed the club's old record for most points in a game (51) and greatest margin of victory (42 points).
The Saints' 55-point victory margin tied for the most in a game since the 1970 merger between the rival AFL and NFL.
Curtis Painter completed 9-of-17 pass attempts for only 67 yards and an interception for the Colts (0-7), who are off to their worst start since 1997.