Tannehill hooked up with Marion Moore on a 29-yard scoring strike in the second quarter, putting the Dolphins ahead to stay, and found Anthony Fasano on a 1-yard TD pass in the third.
The Dolphins (3-3) held a 17-6 lead heading into the fourth quarter, but Sam Bradford spurred the Rams with a quarterback sneak for a score and added a 2-point conversion with 8:30 remaining, cutting the deficit to 17-14.
St. Louis kicker Greg Zuerlein, however, missed a last-gasp, 66-yard field goal try at the final gun and Miami hung on for the victory.
Bradford finished 26-of-39 through the air for 315 yards for the Rams (3-3).
Notable deaths of 2014 [PHOTOS]