Kovalev scored a power-play goal 2:30 into overtime to give Montreal a 3-2 win over Boston on Saturday night and a 2-0 lead in their first-round series. It was also the Canadiens' 13th consecutive victory over the Bruins.
"It seems to me I had so many chances today and I couldn't get the puck in, and last game was the same thing, I missed an open net," said Kovalev, whose seven shots were a team high. "I'm glad it went in."
Thornton got a double-minor for high sticking with 2:17 left in the third when the Bruins forward's stick came up and struck Montreal's Tom Kostopoulos in the face, drawing blood and an automatic -- and ill-timed -- four minutes in penalties.
The Canadiens were unable to score on that advantage but broke through after Reich was sent off for tripping Andrei Markov with 12 seconds remaining in Thornton's second minor.
"We're a team that hasn't hidden behind anything this year and we're not going to start now," Bruins coach Claude Julien said. "We'll take the responsibility for our penalties and we'll move on. I guess the only thing that bothers me is the fact that (Reich) took a stick in the face but because we decide not to embellish, it doesn't pay off. I guess you have to embellish to get a call."
Including the two wins to open this series, Montreal has won 13 in a row dating to the 2006-07 season against Boston, which claimed just one point - a shootout loss - out of a possible 16 in losing eight regular-season games against the Canadiens this season.
"It's just a big relief," said Montreal goalie Carey Price, who stopped 37 shots.
Game 3 is Sunday night in Boston.
"This was definitely one of their best games, but it's going to be even harder to play against them in their home building," Kovalev said.
Schaefer put a backhand past Price 3:58 into the third as Boston finally scored its first goal of the game despite firing 25 shots at Montreal's 20-year-old rookie in the first two periods.
"I think if you look back at the first game they just totally dominated us as far as grit was concerned and along the boards and all those areas that are crucial," Julien said. "We just decided to add some grit in our lineup and they responded well that way."
Bruins defenseman Andrew Alberts appeared in his first playoff game and figured prominently in Montreal's opening goal.
Despite a strong effort in the opening period, Boston went to the dressing room trailing 1-0 after Hamrlik drove a slap shot past Thomas from the left faceoff circle with 1:30 remaining in the first.
The scoring play began with Alberts -- a healthy scratch Thursday -- lining up Montreal's Steve Begin for a check in the Canadiens' zone. Alberts took the brunt of the collision and fell to the ice.
Savard dropped back as Montreal counterattacked and made a vain attempt to block Hamrlik's drive.
Kostitsyn, who scored 34 seconds into his playoff debut Thursday, increased the lead to two 1:30 into the second.
- Price made a left pad save on Thornton's shot with just under five minutes left in the second and moments after Hamrlik drove a slap shot off the left post.
- Canadiens captain Saku Koivu is still recovering from a broken bone in his left foot and did not dress. D Francis Bouillon also remained sidelined by a right ankle injury.