Roloson made 24 saves for the Lightning's (3-2-0) win. Peter Budaj stopped 30 shots for Montreal (1-6-0), suffering his second loss of the pre-season.
Stamkos got his first goal of the exhibition season early in the first. A failed Canadiens clearing attempt saw the puck land in front of Lightning defenceman Bruno Gervais. His shot was stopped by Budaj but bounced out to Stamkos in the slot.
The Lightning sniper would add another just over eight minutes later on a delayed Montreal penalty, finishing off a pass from Martin St. Louis.
Tampa appeared to take a 3-0 lead when a Vincent Lecavalier shot trickled through Budaj's pads. The officials whistled the play down, negating the goal.
The visitors would get that goal back at the 16:43 mark of the second.
Connolly, who entered the night with three points in three pre-season games, took a shot from the side of the net, and then dove to get his own rebound in front and put it past Budaj. He would add his second of the night on a late third period power play.
The Canadiens' chances were there for the taking. Michael Cammalleri hit the post in the first period on a two-on-one with Tomas Plekanec. He later was ready for a break at the Lightning blue-line courtesy of P.K. Subban, only to see the puck bounce over his stick.
There was a two-man advantage for 1:54 midway through the opening period that came up empty. Then, on a late second period power play, David Desharnais set up Cammalleri but the Canadiens winger misfired.
Michael Bournival nearly broke Roloson's shutout with less than six minutes to play, only to see the post take away a potential goal.
The Canadiens and Lightning will each wrap up their pre-season schedules on Saturday night when they meet again in Quebec City.