A limited number of fans were allowed to attend the match at the Toyota Stadium; 2,912 people ultimately turned up.
David Accam's 86th-minute goal was the lone tally of the match, powering Nashville to the first win of its inaugural season in the league.
Both clubs were pulled from the return-to-play tournament in Florida last month after several players tested positive for COVID-19 ahead of the event. That competition, won by the Portland Timbers, ended Tuesday.
Fans were allowed inside the stadium for Wednesday's match despite the continued rise of coronavirus cases in Texas. There have been an average of 7,314 cases per day over the last week in the state, according to the New York Times.
Total cases in Texas have surpassed 528,000.
In order to attend Wednesday's game, supporters had to sign a liability waiver in which they agreed not to pursue legal action against MLS, the teams, or Soccer United Marketing (SUM) - the league's marketing arm - if they contract the disease as a result of their attendance.