The performance came one week after Thomas rushed for 90 yards and two TDs on 11 carries at Kansas City.
"Hopefully I showed these coaches I can play here, I can play at this level," Thomas said. "Just coming in, I told myself this is one of my biggest games. ... I really wanted it so bad and hopefully my performance showed it."
The problem for Thomas is that he put himself in a difficult situation when he signed with New Orleans as a free agent.
So even if Thomas does latch on with New Orleans, he stands little chance of being active from week to week unless he makes himself indispensable on special teams.
Pittman, meanwhile, rushed 21 times for 77 yards.
For Miami, running back Patrick Cobbs made one last bid to avoid final cuts by leading the Dolphins' offense. Cobbs was Miami's leading rusher, with 44 yards on 15 carries. He also led Miami in receiving with 39 yards on five catches. He accounted for two-thirds of Miami's otherwise dismal total of 121 total yards of offense.
"My goal is not to make the practice squad. I want to be on a roster," said Cobbs, the former North Texas standout. "I've been working hard since March to be on the roster and they've got a lot of great backs here in front of me."
After returning the opening kickoff 35 yards, Thomas highlighted the Saints' opening drive with a tackle-slipping 38-yard gain on a screen pass to the Miami 11. From there, he ran three straight times into the line for short gains, squeezing through the pile for the touchdown on the last one from 3 yards out.
"He ran well, picked up some big (first) downs for us, and he's pretty consistent," Payton said.
Very few starters played for either team other than Saints receivers Marques Colston and Devery Henderson.
Colston caught two passes for 17 yards. Henderson did not have a reception.
Martin, who at 37 years old has made a long career as a steady backup, had struggled through much of the preseason. But Payton has stuck with him as the second quarterback, and Martin looked solid against Miami.
Playing the first half, Martin was 11-of-15 for 136 yards and did not throw an interception. He had the Saints in field goal range in the second quarter, but Olindo Mare hit the upright on a 33-yard attempt. Mare also pushed a 55-yarder wide in the third quarter and hit another upright on a 50-yarder.
Beck was 8-of-15 for 63 yards and two interceptions. He was sacked four times.
Palko, trying to hang on as the third quarterback, was 6-of-11 for 27 yards, was intercepted once and had a lot of trouble with the exchange from center. On one drive in the fourth quarter, he mishandled one snap under center and another from the shot gun on a fourth-down play that gave Miami the ball on the New Orleans 43. On the next drive, he fumbled a snap that was recovered by Miami on the Saints 41.
Miami did nothing with either opportunity, however, squandering the first on Beck's second interception. The next Miami drive ended when Beck's pass on fourth-and-26 was batted down in the end zone.
Saints reserve safety Chris Reis, a long shot to make the final 53-man roster, had two interceptions, diving for the second one after linebacker Alfred Fincher tipped Beck's pass.
Fincher, another player on the bubble, had an interception of his own when Back's pass was tipped by reserve defensive end Anton Palepoi.
Reserve Dolphins quarterback Gibran Hamden also was intercepted twice, once by Reis and once by linebacker Dhani Jones.
Reserve cornerback Jason Allen had an interception for Miami, which was one of the highlights of the game for new Dolphins coach Cam Cameron.
"What I enjoyed most about the game was watching those young defensive players play," Cameron said. "You try to maximize the opportunity and evaluate the team and grow as much as you can."
Copyright 2007 by The Associated Press. All Rights Reserved