It's Montreal's longest such streak since winning four in a row from June 13-July 7, 2018.
Miami lost its fifth straight and has been shut out in four of its past five matches.
Montreal dominated the first half, controlling possession (60.8 percent) in the opening 45 minutes while getting six of its 11 shot attempts on goal.
Miami struggled to get its attack going, unable to get past midfield as Montreal stayed tight on the ball.
After an early free kick by Miami in the third minute, Montreal took control.
In the fifth minute, midfielder Djordje Mihailovic fed Choiniere on the right flank and two minutes later, midfielder Victor Wanyama's attempt from the top of the box off a pass from Choiniere went over the net.
McCarthy kept his team in it in the 36th minute, with a header save on Choiniere's long shot from the right side.
Choiniere, playing in his first game since May 15, gave Montreal the 1-0 lead in the 41st minute when his shot from the right wing went far post.
Miami had a better showing the second half, establishing more possession in the attacking third but couldn't find the back of the net.
Gonzalo Higuain, who entered the match as a substitute to start the second half, had his free kick in the 58th minute blocked by Montreal defenders. In the 62nd minute, midfielder Lewis Morgan's attempt from the left side was caught by keeper James Pantemis and six minutes later, Pantemis stopped Jay Chapman's chance from just above the goal mouth.