The win pulled the Fire (15-8-5) within a point of Eastern Conference leader Sporting Kansas City. Chicago has 50 points and third-place New York is right behind with 49.
Montreal (12-15-3), playing its first match in two weeks, dropped its second straight after winning five in a row.
Alex took a pass from Fernandez, split a pair of defenders and beat goalkeeper Troy Perkins to break a 1-all tie in the 61st minute. The Brazilian sent his shot over Perkins and high to the far corner of the net.
Fernandez followed with a 15-yard right-footed shot in the 80th to put the game out of reach. Sherjill MacDonald had tied the match with a nifty header in the 34th, redirecting a pass from Jalil Anibaba into the lower left corner of the net.
Marco Di Vaio gave Montreal a 1-0 lead in the 20th, his fourth straight match with a goal. He took defender Hassoun Camera’s headed centering pass, flicked the ball forward and scored from about 12 yards out. Goalkeeper Sean Johnson fell to his right but could only get a fingertip on the ball.