For the third consecutive game, the outcome was decided in overtime, with Kirk Muller's slap shot from the left circle banking in off Buffalo goalie Grant Fuhr at 11:37.
"This was the closest 4-0 series I've ever seen in my life," Sabre Coach John Muckler said. "Every game could have gone either way."
Montreal Coach Jacques Demers agreed. "We could have just as easily been tied at two games tonight," he said.
The Canadiens have won their last eight games after losing the first two games of their Adams Division semifinal series against the Quebec Nordiques.
"I think we find ways to win, and that's the sign of a good team," Demers said. "It doesn't matter if you get 30 shots against 25. It doesn't matter if at times for 20 minutes you get outplayed. The bottom line is we've won eight in a row and we've found a way to win."
Buffalo, swept in a playoff series for the first time since the Islanders did it in 1977, has been eliminated from the playoffs by Montreal in three of the last four seasons.
New York Islanders 6, Pittsburgh 5--Tom Fitzgerald equaled an NHL record by scoring two shorthanded goals at Uniondale, N.Y., as the Islanders tied the Patrick Division final series at 2-2.
Fitzgerald scored in the last minute of the second period and the first minute of the third to trigger a wild finish to an otherwise tightly played game. The teams scored eight goals in the final 20 minutes after combining for only three in the first 40.
New York's Derek King had the first two goals of his playoff career.
The best-of-seven series will resume Monday at Pittsburgh.
Fitzgerald, who had scored only one goal in 13 previous playoff games, is the seventh NHL player to score two shorthanded goals in a playoff game.