It was the third shutout in four games for Willis and the second straight scoreless draw for Nashville, which took over sole possession of eighth place in the Eastern Conference with the draw. It was also the seventh shutout of the season for Willis moving him into a tie with Eloy Room of Columbus for the top spot in the MLS.
The Boys in Gold also remained unbeaten at Nissan Stadium since the restart.
Dayne St. Clair had three saves for Minnesota United, who remain in fourth place in the Western Conference. It was the third consecutive shutout for the 23-year-old St. Clair and the fourth in his eight starts since replacing injured No. 1 Tyler Miller, who is sidelined for the rest of the season following hip surgery.
Nashville, outshot 17-4 in a 0-0 draw at New England on Saturday, outshot the Loons 8-6 in the first half and had the three best scoring chances.
St. Clair then came up with a big stop in the 26th minute on a right-footed shot by forward Alex Muyl inside the 6-yard box near the right post, and he followed that up three minutes later with a diving save of a right-footed shot by Leal that was headed for the right corner of the net.
Willis didn't have to make a save until the 62nd minute, when he stopped Michael Boxall's close-in attempt off an Aaron Schoenfeld pass by the left post. Willis came up big three minutes later on a chip try on Ethan Finlay, who broke in free into the middle of the box on a through ball by Kevin Molino for the best scoring try of the night.
Minnesota ended up with a 13-10 shot advantage even though Nashville had 55.9 percent of the possession.