Tannehill completed 22-of-35 passes for the Dolphins (5-5), who shook off last week's loss to Tampa Bay and tied the New York Jets for the final AFC Wild Card spot.
Charles Clay hauled in Tannehill's scoring strike, finishing with six catches for 90 yards.
Daniel Thomas rushed for a score, picking up 57 yards on 10 carries as Miami won for only the second time in seven games.
The Chargers (4-6) dropped a third straight as Philip Rivers went 22-of-34 for 298 passing yards, one touchdown and an interception.
Ryan Mathews amassed 127 yards on 19 carries.