With a delayed penalty signaled against Tampa Bay, Perezhogin deflected Mike Komisarek's point shot past goalie Johan Holmqvist to give Montreal its second win in two nights after four straight losses.
Saku Koivu scored his second goal in three exhibition games midway through the third period to tie it at 3. Koivu, who sustained a serious injury to his left eye during the playoffs, drew Montreal even for the third time at 9:56. The goal came moments after Ryan Craig netted Tampa Bay's third power-play tally.
Martin St. Louis had two assists for the Lightning, setting up power-play goals by Eric Perrin in the first and Filip Kuba in the second.
Mathieu Dandenault scored for Montreal at 12:31 of the first to tie it at 1. Andrei Kostitsyn added a power-play goal at 16:40 of the second to get the Canadiens even at 2.
Holmqvist stopped 37 shots for the Lightning (2-1-1). Montreal's Cristobal Huet made 27 saves.
Lightning forward Rob DiMaio left with a concussion and didn't return after he was slammed heavily into the boards by Montreal rookie Guillaume Latendresse early in the first.
Latendresse, a 19-year-old player who had three goals and an assist in his four previous games, was given a major penalty for boarding and was ejected 2:06 in.
That disappointed the sellout crowd of 21,273 that was rooting for the French-Canadian junior -- who had two goals and an assist in the Canadiens' 7-3 win over Ottawa on Monday.