Nashville (5-1-8, 23 points) is 3-0-3 in the past six matches.
Eloy Room had an early save for the Crew (5-3-6, 21 points), who are unbeaten in five matches (1-0-4) and 4-1-4 in the past nine.
Room has four shutouts this season; Willis, six.
Willis came up big in the 94th minute with a two-handed parry off a 20-yard rising shot by Pedro Santos as the Crew dominated the final 20 minutes.
This was the first time the teams have met since the 2020 Eastern Conference semifinal in Columbus when the Crew scored twice in extra time for a 2-0 victory.
The game matched one of the better offenses against a stingy defense. Nashville entered with 21 goals, second in the Eastern Conference to New England's 23. Only the Seattle Sounders (eight) had conceded fewer goals than the Crew (12) in MLS.
Hany Mukhtar, who scored three times in the first 16 minutes Saturday against the Chicago Fire for the fastest hat trick from kickoff in MLS history, nearly had another memorable start.
In the third minute, he ripped a free kick that deflected off the wall. Room had moved to his left but after the ball changed direction, he had to reverse course and made a fully stretched fingertip save at the post.
The Crew's first chance was in the 16th minute when free kick specialist Lucas Zelarayan was fouled 19 yards from goal. With a Crew season record four free kick scores to his credit, he tried to go over the wall but Nashville blocked the attempt.
Willis in the 71st minute matched Room's early stop with a reaching right-handed stop of a low-driven, 25-yard strike from Darlington Nagbe.
It's a quick turnaround as each team is in action Saturday -- the Crew at Atlanta United while Nashville hosts FC Cincinnati.