Vanek scores with 2:21 left in the period, assisted by Pacioretty and Andrei Markov.
Pacioretty with a chance at his second goal of the game, but Rask makes the save with 0:15 left to play.
The 2nd period ends with Montreal up 3-0 in a must-win game.
Montreal back ahead in both shots (23-18) and hits (31-26) going into the 3rd period.
Montreal will force a game seven in Boston on Wednesday with a win here tonight.
Third period begins with Boston needing to climb back from a 3-0 deficit.
Great save by Rask on a Montreal two-on-one as the net comes off the pegs.
Montreal chance comes after solid Boston scoring opportunity at the other end.
Canadiens put one off the side of the net, keeping the pressure on with 16:00 left in the game.
Montreal back on the power-play after Milan Lucic gets called for tripping P.K. Subban
Boston kill the penalty but need to net three goals in the next 14 minutes.
Bruins called offside with 11:14 to go in the game.
Canadiens now out-shooting Bruins 27-20 in the 3-0 contest.
Montreal controlling the puck through the halfway mark in the period.
Boston almost puts it in the net, but ref waving no goal
Puck flies up over Price's head, bounces off post and rolls on the line before being batted away by Montreal.
Refs discussing the near-goal that would put Boston within two.
Official: No goal. Game still MTL 3-0 BOS
8:30 left to play in Game 6.
Puck deflects out of play after a shot by Iginla. 7:30 Left for Boston to get back into the game.
Boston calls a timeout. Bruins need three in the next five to avoid a seventh game.
The Canadiens take a 4-0 lead with an empty netter as Rask heads to the bench.
MTL Thomas Vanek scores an unassisted empty-net goal to put Boston down by four with as many minutes left.
Correction: Vanek's fifth goal of the playoffs was assisted by David Desharnais.
Rask stays on the ice as the game winds down to 2:30 left.
One minute to go as the hometown fans are off their feet.
Montreal and Boston will play their fourth Game Seven against each other since 2004 on Wednesday. Canadiens have won two of the past three.
But not before the game stops for a near-scrap. Garbage flies onto the ice with 0:24 left in the game.
Rest of the game will be played four-on-three after a handful of penalties.
BOS Iginla goes away for roughing, Chara for roughing and slashing, while MTL Weaver sits for slashing.
Time runs down and the final horn sounds, final score MTL 4-0 BOS
Price earns the shutout to send his team to a seventh game in the series.