Nearby police officers engaged Connor Betts, 24, shortly after hearing gunfire, as he tried to make his way into a crowded bar.
Dayton police chief Richard Biehl said that had he made it through the door, the loss of life would have been "catastrophic".
The gunman's motives are unclear.
At least 27 people were injured in the shooting, the second such attack in the US within 24 hours.
Betts fired his first shot at 01:05 local time (05:05 GMT) in the Oregon district of the city centre, Mr Biehl said. Dozens more rounds followed.
