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Montreal's Alex Kovalev, second from right, scored his first career overtime winner in the playoffs Saturday to lift the Habs to a 3-2 win over Boston. ((Ryan Remiorz/Canadian Press))

The NHL's top power-play unit during the regular season sputtered along hopelessly through 60 minutes of regulation, but finally clicked when it mattered most — in overtime.

Alex Kovalev scored the overtime winner to give the hometown Montreal Canadiens a 3-2 win over the Boston Bruins Saturday night in Game 2 of their Eastern Conference quarter-final.

Montreal went 0-for-6 with the man advantage and squandered a 2-0 lead by giving up two goals in the third period, but Kovalev bailed out the Habs when he drove a bullet of a shot past Boston goalie Tim Thomas at 2:30 of the extra frame.

It was Montreal's first power-play goal in 13 opportunities in the series.

The best-of-seven quarter-final now shifts to Boston for Game 3 on Sunday (CBC, CBCSports.ca, 7 p.m. ET) with Montreal sitting on a 2-0 lead.

"It was a tight game where whoever got the bounce would win," said Kovalev. "We expected them to come out better and they did.

"We have to be more patient and not open up too much. And most of all, stay out of the penalty box."

Rookie goalie Carey Price, outstanding through the first two periods but somewhat shaky in the third, made 39 saves to earn the win.

Price said the key was getting refocused for overtime after a stressful third period.

"We knew we couldn't panic and we couldn't let ourselves get stressed and running around. Fortunately we got a power play and we buried it," Price told Hockey Night in Canada.

Montreal has now won all 10 meetings with Boston this season and 13 in a row overall.

"We feel we deserve better," said coach Claude Julien. "Aside from the penalties, we battled hard and our penalty killing was outstanding.

"We gave ourselves a chance and that's something we can build on."

The Bruins, thoroughly outplayed in Game 1, were buzzing right from the opening faceoff Saturday, and swarmed the Canadiens' net on an early power-play opportunity, only to be thwarted by Price.

Boston was skating stride for stride with Montreal and appeared to be growing in confidence. But Canadiens defenceman Roman Hamrlik, celebrating his 34th birthday, stunted the Bruins' momentum when he blasted a shot by Thomas late in the period on a goal the Boston netminder should have stopped.

Montreal padded its advantage early in the second period.

Kovalev amazingly kept possession of the puck for a good 20 seconds, fighting off several Bruins in the process, as he skated inside the Boston blue-line, before the puck landed on the stick of Sergei Kostitsyn who skillfully slotted it past Thomas.

Andrei Kostitsyn nearly made it 3-0 late in the frame, only to be denied by Thomas on a breakaway.

Boston's persistence paid off when they notched a goal early in the third. Price uncharacteristically gave up a big rebound off a weak shot from the point and Peter Schaefer drove to the net and banged the puck home.

The goal gave the Bruins new life and took the vocal Montreal crowd out of the game, and after Kovalev failed to score on a short-handed breakaway and picked up a slashing penalty, Boston tied the contest while enjoying a two-man advantage.

Boston moved the puck around quickly inside the Canadiens' blue-line and Price overplayed a Marc Savard pass from the point to Marco Sturm, allowing the Bruins defenceman to slip the puck across the crease to a wide open David Krejci, who scored into an empty net.

"It gets frustrating taking slashes and cross-checks," said Kovalev. "It was a selfish penalty, but I was able to get it back."

Montreal fought back and came within an inch of securing a win when Patrice Brisebois's slapshot from the top of the circle rang off the post with one one-hundredth of a second left in regulation.

"We didn't really talk much about what happened (in the third period). We just knew we had to come out and play our game. We got running around a bit in the third and we settled down and got the win," Price said.

The Bruins fell into penalty trouble early in the extra frame, but were bailed out by Thomas who made a great pad save to deny Kovalev from in close.

Boston didn't do itself any favours when winger Jeremy Reich was called for a tripping penalty, and the Habs made the Bruins pay for their lack of discipline when Kovalev's wicked blast found the back of the net.

Forward Phil Kessel was a healthy scratch for Boston, while defenceman Dennis Wideman did not dress after receiving a lower-body injury in Game 1.

With files from Canadian Press