The National Football League began using overtime to determine the winner of regular-season games in 1974 and this was only the third time such a contest has ended on a safety.
Cincinnati wasted a second-half comeback that saw the Bengals take a 20-17 lead on Mike Nugent's 54-yard field goal with 1:24 to play in the fourth period.
Miami tied it with 11 seconds remaining on a field goal of 50 yards by Caleb Sturgis and the Dolphins then ended a four-game losing streak thanks in part to another big play on special teams.
At the end of the Dolphins' second possession in overtime, Miami punter Brandon Fields pinned the Bengals back at their 8-yard line.
Dalton then threw two incompletions and on third down Wake escaped with an inside rush from his defensive end position and hit the Cincinnati quarterback as he stood at the goal line.
A safety was called on the play and that call withstood a video review with it was determined the ball was barely behind the goal when Dalton was tackled.
Cincinnati suffered its first loss in five games and fell to 6-3. Its lead over Baltimore in the AFC North was reduced to two games. Miami advanced to 4-4.
The last time an overtime game was decided by a safety came in 2004 when Chicago defeated Tennessee 19-17. Minnesota also won over the Los Angeles Rams thanks to an overtime safety in 1989.
A 94-yard interception return for a touchdown by Brent Grimes gave Miami a 17-3 lead midway through the third period, but Cincinnati came back on touchdown runs of 3 and 35 yards by Giovani Bernard.
Miami intercepted Dalton three times and pulled out the victory despite being outgained 465 yards to 345. Cincinnati ran 32 more plays than did the Dolphins.
Miami quarterback Ryan Tannehill completed 20-of-28 passes for 208 yards without throwing a touchdown or an interception. Dalton went 32-of-53 for 338 yards.