"My eyes were downfield, and he was there pretty quick," Dalton said, adding he thought he was out of the end zone.
According to STATS, Minnesota's Mike Merriweather had the first NFL overtime safety in 1989 against the Los Angeles Rams, and Chicago's Adewale Ogunleye had the second against Tennessee in 2004.
"I don't think anyone expected the game to end on a safety," Miami quarterback Ryan Tannehill said.
The Bengals lost despite totaling 28 first downs and 465 yards while holding Miami to three third-down conversions. They could have tried a 56-yard field goal in overtime but punted to the Dolphins instead.
"We had a chance, maybe," Lewis said, "but we felt better about pinning them down."
Lewis made another questionable decision at the end of the first half. When the Bengals started from their own 15 with no timeouts and 45 seconds left, he decided against running out the clock.
His aggressive approach backfired when Dalton's pass was intercepted by Dimitri Patterson, setting up a 36-yard field goal by Caleb Sturgis to put Miami up 10-3 at halftime.
Mike Nugent kicked a 54-yard field goal with 1:24 remaining in regulation to put the Bengals ahead, but Miami answered with a 50-yard drive, and Sturgis made a 44-yard field goal with 11 seconds left to force overtime.
Brent Grimes returned an interception 94 yards for a touchdown to put the Dolphins up 17-3 midway through the third quarter, but they squandered a two-touchdown second-half lead for the second time in five days. On Sunday in a loss at New England, they were outscored 24-0 in the final 24 minutes.
Cincinnati's Giovani Bernard scored on an electrifying tying 35-yard touchdown run in the third quarter that covered perhaps twice that much ground. He started right, doubled back left, weaved up the sideline, cut back across the middle and somersaulted in the end zone, leaving Dolphins sprawled in his wake all along the way.