Smith completed 17-of-27 passes for 190 yards and ran for 44 more on 10 carries, including a 7-yard TD scramble, as the Jets (8-8) won consecutive games for the first time this season.
Smith led New York on a pair of second-quarter touchdown drives to seal the win.
Bilal Powell rushed for 76 yards and also completed a key pass in the fourth quarter.
The Dolphins (8-8) missed the playoffs for a fifth consecutive year after dropping a second straight to end the season.
Ryan Tannehill was picked off three times, finishing with 204 passing yards and a TD on 20-of-40 efficiency.