Daryl Dike's second-half brace proved decisive as Orlando climbed into fourth in the Eastern Conference.
But it came on a day when five other games were postponed as teams in North America boycotted matches over racial injustice following the shooting of Jacob Blake in Wisconsin.
The scheduled clashes called off were Inter Miami-Atlanta United, Dallas-Colorado Rapids, Real Salt Lake-Los Angeles FC, San Jose Earthquakes-Portland Timbers and LA Galaxy-Seattle Sounders.
Orlando's game with Nashville was already in progress when the remaining MLS matches were postponed.
Nashville took the lead away from home at Exploria Stadium, David Romney heading in Hany Mukhtar's set-piece in the 15th minute.
But Orlando levelled just six minutes later through Christopher Mueller, who headed in Joao Moutinho's cross from close range.
Dike delivered a key double in the second half for the hosts, who bounced back after a loss to Inter Miami following their MLS is Back Tournament final defeat.