After a scoreless first quarter, it was the visitors who took the lead early in the second thanks to Mike Nugent's 31-yard field goal, but the Dolphins soon seized the initiative as Ryan Tannehill jumped over the line with the ball.
Caleb Sturgis kicked the extra point, and a field goal from 36 yards extended that lead to seven points before half time.
The 21-year-old running back got the visitors back in the game with a three-yard score before the end of the third quarter, but his second - an 35-yard surge - drew his team level early in the fourth.
Nugent and Sturgis traded field goals before the end of regulation play, leaving the two teams tied on 20-20.
The match was decided when Wake beat Kevin Zeitler to bring down Dalton in the endzone, stealing two points and the win, which snaps their three-game losing streak.
Meanwhile, the Bengals are 6-3 at the top of the AFC North.