Nashville (5-4-3, 18 points) stretched its unbeaten home game streak to 22 games.
Willis hit the long diagonal to Muyl, who cut in on his left foot and hit a beauty that Montreal goalkeeper Sebastian Breza never had a chance to get.
Nashville looked like it would have a chance to extend its lead before half-time, but Montreal (6-4-2, 20 points) had the last chance at the break.
Montreal opened the second half with consistent pressure, pushing to equalize. However, Nashville was able to beat the pressure, and Mukhtar found the back of the net in the 51st minute. He pushed the ball deep for C.J. Sapong, who fought off a tackle in the box and squared it back to Mukhtar, who then slid it past Breza.
Kamara brought the visitors back within one in the 55th minute with his third goal of the season. It came after Willis cleared a Victor Wanyama cross right into Kamara. The resulting deflection went in as Kamara and Willis collided in the box.
Montreal continued to push, but could not fully break down Nashville's defense.
Willis finished three saves on four shots on target. Breza finished with three saves on five shots.