The Revolution (5-3-7, 22 points) extended their unbeaten streak to 2-0-2 as Matt Turner made one save for his sixth shutout of the season.
Nashville (4-5-5, 17 points) tied for the second straight match as Willis also earned his sixth shutout -- despite the Revolution having a 17-3 shot advantage.
Earlier Saturday, Nashville announced that an unnamed player tested positive for COVID-19 and self-isolated immediately. The remaining players and staff received two consecutive negative results and it was determined the match could be played.
Daniel Rios, who scored in each of the past two Nashville games, did not play. He sustained a leg injury in the previous match and was not medically cleared.
Rios was one of seven first team players unavailable and Nashville relied on its sturdy defense to offset an already struggling offense that has scored 11 goals, tied for second-fewest in MLS, with just two goals in eight road matches.
The Revolution's lone shot on target in the opening 45 minutes was a dipping 22-yarder by Tajon Buchanan that forced Willis to parry the ball over the crossbar in the 7th minute.
Early in the second half Willis came through again to get his fingertips on an unmarked shot by Gustavo Bou from the edge of the 6-yard box.
Meanwhile, Turner wasn't tested until the 53rd minute when he made a lunging stop with his left hand after a restart flicked off a Revolution player and changed direction.
Ten minutes later it was Willis' turn to shine, stopping Buchanan's header by tipping the ball over the frame. Buchanan was frustrated again by Willis at the left post a few moments after that.
Nashville hosts Minnesota United on Tuesday. The Revolution are home to Toronto FC on Wednesday.