Brees completed 33-of-43 passes as the Saints erased a 14-10 halftime deficit and dominated thereafter to advance to the NFC divisional round.
New Orleans, which was bounced from the playoffs in a wild card-round loss to Seattle last season, now goes on to face San Francisco next week.
Pierre Thomas, Darren Sproles and Chris Ivory together racked up 164 rushing yards on 31 carries. The trio also combined for 10 catches for 89 yards and a score for the NFC South champs.
The Lions, meanwhile, fell short in their first playoff appearance since 1999.
Matthew Stafford piled up 380 yards and three touchdowns on 28-of-43 efficiency in his playoff debut for Detroit. His performance was marred, however, by two interceptions in the fourth quarter.