Tannehill connected on 22-of-28 passes for 220 yards without an interception and also ran for 52 yards on eight carries, outplaying the Jaguars' Chad Henne, who was a Dolphins signal-caller for four years.
Reggie Bush racked up 104 rushing yards as Miami reeled off the game's final 24 points to win going away.
On defense, the Dolphins stymied Jacksonville on downs three times en route to the victory.
Henne was held to 18-of-34 passing efficiency for 221 yards as the Jaguars (2-12) lost for a third straight time.
Jacksonville is in danger of finishing with the worst mark in team history following their 4-12 showing in the inaugural 1995 season.
Notable deaths of 2014 [PHOTOS]