The Predators (6-1-0) controlled the first period and O'Reilly opened the scoring when he banged in a rebound off Jordan Tootoo's slap shot from the point.
But it was Winnipeg (3-3-1) that came to life after the fight, outshooting the Predators 16-3 as Andrew Ladd tied things by flipping in Bryan Little's backhand home after it bounced away from Nashville goalie Anders Lindback.
The Jets couldn't connect on the power play. Nashville's David Legwand took advantage of a slashing penalty handed to rookie Mark Scheifele to score the Predators' go-ahead goal at 7:28 of the third period.
Scheifele made up for it at 13:07 when he tied the game with his fourth goal of the preseason.
Notes: Nashville coach Barry Trotz is a Winnipeg native. ... The game was also a home game of sorts for Colin Wilson, who was raised in Winnipeg, and Tootoo, who was born in Winnipeg.