Saku Koivu scored in the shootout and Montreal beat Boston 3-2 on Saturday night, completing a sweep of the season series.
Koivu put a backhander past Tim Thomas on the Canadiens' third attempt and was mobbed at center ice by his teammates amid the roar of the sellout crowd of 21,273.
Montreal won all eight of their games against the Bruins this season and extended its win streak against Boston to 11. The streak is the Canadiens' longest against the Bruins in the 84-year rivalry between the two teams. Montreal won 10 straight against Boston during the 1944-45 season.
"When you get 16 points, that's a big difference," Koivu said of the Canadiens' eight wins against Boston. "Obviously that's a big reason we're first in the standings right now."
Montreal, which also leads the Northeast Division, has 94 points with six games remaining.
"We need to get every point we can," Price said. "Even though we had one point going into the shootout, we knew we had to get that other one. Those are the points you're going to need when it comes down to the last two games."
Marc Savard and Petteri Nokelainen scored for the Bruins, who are tied with Philadelphia for the final two playoff spots in the East with 84 points and seven games remaining. Ninth-place Washington has 82 points and six games remaining, while 10th-place Buffalo is two points back and plays two of its seven games against Boston.
The Canadiens took a 2-1 lead midway through the opening period despite being outshot 16-7 in the first.
Nokelainen drew Boston even at 2 with his seventh goal 9:33 into the second.
"That shows that we can hang with these guys," Thomas said. "I thought we were going to get over the hump tonight."
Defenseman Mike Komisarek and left wing Guillaume Latendresse were out of the Canadiens' lineup after both were injured in Thursday's 4-2 win in Boston.
Komisarek, the Canadiens' leader in hits and blocked shots, will be sidelined for two weeks because of what the Canadiens are calling a lower body injury, which is believed to be affecting either his lower back or groin. Latendresse is day to day with neck spasms.
Steve Begin returned for Montreal after missing 11 games because of a groin injury. The pesky forward fought with Shane Hnidy with 2:55 left in the second moments after he flattened the rugged defenseman with an open-ice hit in the Bruins zone.
Markov gave Montreal an early lead with his 15th goal 2:20 in. The Canadiens defenseman scored unassisted as he jumped on Kessel's giveaway in the Bruins zone and drove a slap shot past Thomas.
Savard scored on a 4-on-4 at 8:36 to tie it at 1. The Bruins' playmaking center raced behind the net to beat Price on a wraparound as the Canadiens goalie was unable to keep the puck out with his left pad as he scrambled vainly across the crease.
Kostitsyn restored Montreal's lead at 9:49 when he gathered a rebound of Mark Streit's shot and moved around Thomas to put a backhand inside the right post for his 23rd goal.
Notes: Canadiens coach Guy Carbonneau pulled Price for a faceoff in the Bruins zone with 1.4 seconds remaining in overtime. Koivu won the draw but Montreal was unable to get a shot off. ... The Canadiens have 333 wins, 253 losses, 103 ties and four overtime/shootout losses in 693 games overall against Boston.