The defense also had a big night, with rookie cornerback Sean Smith coming up with a spectacular one-handed interception and the pass rush harassing Joey Harrington, who looked as indecisive as he did during his one season with the Dolphins.
The Dolphins almost capped their preseason with a shutout, but they gave up a 55-yard punt return for a touchdown to Rod Harper late in the fourth quarter.
Chad Henne led the one touchdown drive for the Dolphins as he completed his first six passes, the longest a 24-yard dart to Ted Ginn Jr. to the 5-yard line. On the next play, Cobbs scored after running to the right and then cutting back.
Both Henne and Pennington were effective against New Orleans, but the Dolphins had trouble sustaining many drives.
It didn't matter, though, because the defense made Harrington look bad.
With Drew Brees sitting out the game, Mark Brunell started at quarterback for the Saints and he led them into Dolphins territory on both of his drives. But Jason Taylor batted down a pass on fourth down to stop one drive and Smith stopped the other with his acrobatic interception.
New Orleans' John Carney missed a 33-yard field goal in the final seconds of the first half to waste the Saints' best scoring opportunity.
The Dolphins ended up with a whopping eight sacks, all against against Harrington. Tony McDaniel and Charlie Anderson each had two sacks to lead the way, while Reggie Torbor, Rodrique Wright, Lionel Dotson and William Kershaw had one apiece.