Bryce Duke put the hosts ahead at Saputo stadium with a 22nd-minute strike after Jules Vilsaint's perfectly weight pass on the counterattack. Vilsaint then put his name on the scoresheet by playing a slick one-two with Ariel Lassiter before cutting inside his marker and angling a shot into the far corner.
The visitors suffered a scare as Lionel Messi limped off the pitch in the 42nd minute, having appeared to injure his left knee following an ugly challenge from George Campbell, reports Xinhua.
In his absence, Matias Rojas stepped up to curl home a free-kick after Suarez was fouled by Samuel Piette.
Messi, who was playing for the first time in Canada, returned to the pitch almost immediately after Rojas' strike. Inter's fans had even more reason to cheer four minutes later when Suarez tapped home at the far post after Julian Gressel's cross was unwittingly flicked into his path by Duke.
Suarez has now scored 12 goals and given seven assists in 15 matches across all competitions since joining Inter Miami in January.
The Florida outfit continued to dictate play after the interval and Rojas turned provider as his clever run and pass set up Ben Cremaschi to tap home just before the hour.
The visitors withstood a tense final half hour to secure their fifth straight MLS victory and maintain a three-point lead over second-placed Cincinnati in the 15-team Eastern Conference. Montreal are 12th, 12 points further back.