Cobbs, a long shot to make the team, provided the winning margin when he scored on a 3-yard run with 3:46 left and then added the two-point conversion on a run as Coach Cam Cameron decided against going for a tie.
The game-winning drive, which erased a 17-10 deficit and covered 69 yards, was engineered by rookie John Beck, who completed three passes on the drive.
Chatman, meanwhile, had the biggest play of the game when he took what looked like a run that was going nowhere and bounced it outside all the way for a 74-yard touchdown in the third quarter.
Chatman's run came after a 1-yard touchdown run by Alvin Pearman had given Jacksonville a 17-3 lead.
But the results weren't impressive as Miami finished with only four first downs and 64 total yards.
The result was a 10-3 deficit at halftime.
Green played the entire first half and finished 6-of-15 for 60 yards with one interception.
But Green wasn't helped by an offensive line that allowed constant pressure, and the one interception came off a low pass that went off the hands of Dolphins wideout Derek Hagan.
The drive began in the first quarter and was kept alive when Vonnie Holliday was flagged for roughing the passer as Leftwich was throwing an incomplete pass on third-and-20 from the Jacksonville 15.
A 32-yard Josh Scobee field goal made it 10-0 before Feely cut the lead to seven again.