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Kostitsyn assisted on Plekanec's tiebreaking goal with 3:59 remaining which gave Montreal a 4-3 win over the Ottawa Senators on Saturday night.
Plekanec put a rebound of Kostitsyn's shot past Brian Elliott after the Canadiens rallied from a 3-1 deficit. Ottawa had built its lead with two goals scored 53 seconds apart midway through the second period.
"It was a great play by Andrei," Plekanec said. "He went to the net. He drove there and I just followed and got lucky off the rebound."
Kostitsyn tied it at 3 late in the second after Jeff Halpern got the Canadiens' comeback started with his second goal of the season at 13:39.
"He's a difference-maker this year," said Plekanec, who assisted on Kostitsyn's goal.
"I didn't face a whole lot of work, but it just shows our guys are working out there to help me," said Price (3-1-1), who has started each of the Canadiens' games.
Milan Michalek had two goals, and Erik Karlsson also scored for Ottawa (1-3-1). Daniel Alfredsson and Jason Spezza both had two assists.
"It's just the small things right now," Karlsson said. "I think we battled hard and we played good, it's just that we've got to close the game off a little more there when we have a two-goal lead and play a little bit smarter. Overall, I think we're on the right track here."
Elliott stopped 33 shots in his first start of the season. Elliott made 19 saves in relief of injured starter Pascal Leclaire in the Senators' 3-2 win over Carolina on Thursday.
Robin Lehner, recalled from Binghamton of the AHL on an emergency basis earlier Saturday, started the third after Elliott broke a skate between periods. The 19-year-old Swede made the first three saves of his NHL career - including a big stop on Michael Cammalleri - before Elliott returned 4:42 in with a new pair of skates.
"It was nice for me to have my first little bit of a game played here in the show," Lehner said. "And an extra bonus, I think I'm the youngest Swedish goalie ever to play in the show so I'm happy about that. I couldn't have done more."
Gionta scored 1:06 in on Montreal's first shot. The Canadiens captain beat Elliott with a deke to his backhand after winning a race for the puck when Michalek was unable to handle Alfredsson's pass back to the right point.
Michalek tied it at 1 midway through the first period, putting home a loose puck for his first goal of the game.
Ottawa went up 2-1 on Karlsson's first of the season 10:20 into the second. Michalek scored his second of the game at 11:13 to increase the lead to two goals.
Halpern got credit for his second of the season when his back pass went in off the skate of Senators defenseman Chris Campoli.
Kostitsyn drew Montreal even at 3 at 17:29 when he roofed a shot past Elliott.
Price kept the game tied with a big glove save when Peter Regin elected to shoot on a 2-on-1 rush with 1:45 left in the second.
NOTES: Lehner was chosen 46th overall by the Senators in the second round of the 2009 draft. ... Canadiens LW Mathieu Darche returned to the lineup for the first time since Montreal's season opener. C Tom Pyatt didn't play.