Brees led the Saints to victory despite surrendering a pair of interceptions while Darren Sproles added 75 rushing yards on seven carries as well as making five catches for 56 yards.
New Orleans (3-1) notched its third straight win after losing its season opener at Green Bay.
The Jaguars (1-3), meanwhile, went down to their third straight loss.
Blaine Gabbert had a rough day in his second career NFL start, ending with 196 yards, one touchdown and one interception on just 16-of-42 passing.
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