After going scoreless in a 1-0 loss to the Los Angeles Galaxy and a draw with the Vancouver Whitecaps, NYCFC (1-1-1, 4 points) took control early after celebrating their run to the MLS Cup in December.
Callens scored NYCFC's first goal of the season in the seventh minute and Rodriguez struck in the 20th minute. Talles Magno also tallied in the 64th minute and Thiago Andrade scored in the 83rd.
NYCFC goalkeeper Sean Johnson finished with two saves.
Zachary Brault-Guillard scored in the 52nd minute after entering the match as a substitute in the second half for CF Montreal (0-3-0, 0 points).
CF Montreal goalie Sebastian Breza made three saves.
NYCFC gained a two-goal lead by capitalizing on CF Montreal's defensive miscues.
In the seventh minute, Keaton Parks intercepted a clearing attempt by Montreal defender Kamal Miller and whipped the ball to Magno. Magno controlled the ball with his chest and headed it to Callens, whose left-footed shot from the center of the box sailed over Breza.
NYCFC took a 2-0 lead after Montreal failed to clear and Rodriguez used his finesse to hammer a right-footed shot from well outside the box into the bottom left corner.
Rodriguez's goal occurred seven minutes after Joel Waterman overran the ball on a corner kick and missed an easy chance at tying the game for Montreal.
Three minutes after missing the net. Brault-Guillard scored when he slipped past NYCFC's Malte Amundsen down the left side. He then slid a right-footed shot into the bottom right corner from close range after getting a long cross from Djordie Mihailovic.
Three minutes after Braut-Guillard scored, Johnson made consecutive saves on Matko Miljevic and Mihailovic. Montreal had a goal disallowed after Robert Thorkelsson was ruled offside in the 61st minute, and NYCFC took a 3-1 lead when Magno finished off a header from the middle of the box.
NYCFC finished it off when Andrade sent a right-footed shot from the middle of the box into the net after pressuring Mihailovic into a turnover near midfield.