The Thompson touchdown came one play after Fiedler connected with Chris Chambers on a 38-yard completion down the right sideline, the first-team offense's first long completion of the preseason.
The Dolphins' other points came courtesy of a 46-yard field goal by Olindo Mare right before halftime. Mare also missed a 51-yard attempt in the third quarter when his kick came up short.
The Dolphins put the game away late in the second quarter with Lee's touchdown and Mare's field goal, which was set up by Ayanbadejo's fumble recovery on a kickoff.
New Orleans' only touchdown came on a 6-yard pass from Todd Bouman to Michael Lewis in the second quarter and tied the score at 7-7 until the Dolphins took charge with 17 points the rest of the quarter.
The Dolphins didn't score in the second half with Lon Sheriff at quarterback, but it didn't matter.
As expected, the starters were out of the game by the middle of the first quarter, although Seth McKinney played into the second half.