Miami improved to 8-3 and took over the top spot in the division by itself when the New York Jets fell to New England. Denver slipped to 6-6.
Playing in front of a sparse crowd at Pro Player Stadium, the Dolphins were less than 14 mintues away from their second straight shutout loss at home.
But Jay Fiedler threw an 11-yard touchdown pass to rookie Chris Chambers 1:15 into the fourth and Mixon went untouched with his interception to give Miami a 14-10 lead with 9:51 remaining.
Denver then fumbled the ensuing kickoff and Miami turned the miscue into a one-yard touchdown run by Lamar Smith with 8:59 remaining.
The Dolphins' defense did the rest, shutting down quarterback Brian Griese in his return home. The Broncos' quarterback is the son of former Miami Hall of Fame quarterback Bob Griese.
Denver running back Terrell Davis returned from a two-game absence and carried 20 times for 97 yards. But the Broncos took a hit in their quest for a postseason berth.