NEW ORLEANS — One of the N.F.L.’s more incontrovertible contentions, supported by more than a decade of empirical evidence, is that good things tend to happen to the New Orleans Saints when the football leaves Drew Brees’s hand.

That hand has thrown for more yards and touchdowns than anyone else who has played for the Saints, elevating them to prominence and delivering a Super Bowl. This season, that hand threw the second-fewest passes since Brees arrived in New Orleans, and instead continually thrust the ball into the bellies of Mark Ingram and Alvin Kamara, the running backs responsible for transforming the Saints’ identity.

The Saints have transformed from a team that depends on Brees to a team that benefits from his talent, but in no way does that diminish his ability to power them to victory. In outlasting the Carolina Panthers for the third time this season, with a 31-26 playoff win amid the din of the Superdome on Sunday, Brees reaffirmed his primacy.

There have been other instances across his playoff career when Brees sparkled, but those were back when the offense revolved around him and teams designed game plans to neutralize him.