Colston's 7-yard TD grab from Drew Brees (21-of-32, 298 yards, three TDs, one interception) in the third quarter put the Saints ahead 28-17 and New Orleans (4-5) hung on down the stretch to knock the Falcons (8-1) from the ranks of the undefeated.
The catch gave Colston 55 scoring grabs for the Saints, tying him with Deuce McAllister for the most in team history.
New Orleans' defense -- porous throughout most of the season -- came up big in the closing moments, first frustrating Atlanta on four tries to cross goal from the New Orleans 2-yard line with 2 minutes left.
The Saints also turned back a last-chance try by the Falcons, securing their second straight win.
Swim Week Miami Beach 2014 [PHOTOS]