Nashville (7-6-7, 28 points) has three wins and a tie in the past four games to move ahead of the New York Red Bulls by two points into seventh in the Eastern Conference with three games left.
Montreal (7-12-2, 23 points) remained ninth with two games remaining, at the moment above the cutoff line that will see 10 Eastern Conference teams reach the playoffs. The Impact are 2-8-1 in their past 11 matches.
Nashville's Joe Willis made two saves for his ninth shutout. Clement Diop made five saves for Montreal, which is playing its home games at Red Bull Arena because of Canada's COVID-19 border restrictions.
Muyl tumbled but immediately regained his composure and sent the free kick past three Impact players with a perfect lead to Leal near the top of the box.
Leal took the pass in stride and slotted a left-footed short from 13 yards for his third goal to tie Hany Mukhtar, Daniel Rios, and Walker Zimmerman for the team lead. Muyl earned his first assist of the season.
Facing a deficit proved to be a problem for Montreal against one of the league's stingiest defenses. Nashville's 18 goals allowed are the third fewest in the Eastern Conference.
The Impact are 2-10-1 when opponents score first and have lost all nine games when trailing at the half. Nashville is 7-2-2 scoring first and 4-1-0 with the halftime lead.
Nashville heads home to oppose the Chicago Fire on Saturday. Montreal hosts Orlando City on Sunday.