The Fire took all three points off Montreal, bringing the clubs within four points of each other in the standings.
Chicago took an early lead when Lindpere scored in the sixth minute. Montreal cleared Chicago's free kick, but the Fire were able to work it back in, and the Estonian midfielder was given the time to tee up a shot which took a deflection before going in.
Duka doubled up for the Fire a few minutes later, rushing through the Montreal defense - with a fortunate bounce helping him along the way - and slotting home a nice finish to make it 2-1.
Felipe Martins hammered home a left-footed strike in the 57th minute to pull Montreal back to within one, but that would be as close as the Canadian side would come.
The win puts Chicago within two points of the final playoff spot in the East.