The scoring winger from Ste-Justine, Que., had been acquired in the summer from the Calgary Flames, where he had struggled last season under coach Mike Keenan, and was coming to a team with high expectations after finishing first in the Eastern Conference.
But if Tanguay's play through his first 10 games as a Canadien is an indication, it may be that he plays his best with the pressure on high.
Tanguay had six goals and five assists and was plus-6, tied with linemate Saku Koivu for second in team scoring behind defenceman Andrei Markov, who had 13 points for the 8-1-1 Canadiens.
On Wednesday, Tanguay was named the team's player of the month for October.
"You look at what Andrei Markov has done and he's been pretty much our best player since the start of the season," Tanguay said. "I'm just here to help make this team successful.
"The rest are all bonuses, but it's nice."
The Canadiens were looking to add depth to their attack when they picked up Tanguay and centre Robert Lang, but expected it would take some time for them to adjust to a new team.
Tanguay and Koivu clicked right away, first with Guillaume Latendresse on their wing and more recently with the speedy Christopher Higgins.
"For the first 10 games, for sure it's a surprise because I'm usually a slow starter," added Tanguay. "We still feel as a line - me, Saku and now with Chris - that we can play better.
"We can improve in certain areas. We can be more consistent. That goes for the whole team. I know the record may not be 8-1-1 every 10 games, and we can improve."
There were doubts at the start of the season about putting Tanguay and Koivu together. They play similar styles. Both like to hold onto the puck to make plays. But rather than getting in each other's way, they've become a dangerous twosome with strong numbers on attack and on defence. Koivu is a team-best plus-9.
"One thing is that we got a couple of goals right away, in the second game of the season," said Koivu. "Especially for him, as a newcomer, it took some pressure off.
"And when you get some goals, you're more relaxed on the ice and then you get some confidence. Sometimes you don't need a lot of games with a guy to get some chemistry and with Alex, I find he's really easy to play with, with his vision and the way he can hold onto the puck an extra second to create time and room for me."
The 28-year-old Tanguay's best years were with his first team, the Colorado Avalanche, with whom he had a career-high 79 points in 2003-04 and a career-best 29 goals in 2005-06. He slipped to only 18 goals and 58 points last season, his second with the Flames, where his power-play time was reduced.
With the Avalanche, he had star centres Joe Sakic and Peter Forsberg as linemates, and now is thriving with another gifted centreman in Koivu.
"Saku plays very similar to Joe," he said. "He likes the quick passes and give-and-go's.
"He's fun to play with. It's hard for me to rank them, but it's going good."
Their strong play was timely because the top line of Tomas Plekanec, Alex Kovalev and Andrei Kostitsyn couldn't find the net until they broke out for a combined 10 points in a 5-4 comeback win over the New York Islanders on Saturday night.
The Canadiens, with 23 healthy players, are in a five-day break before games Friday night in Columbus and Saturday night in Toronto.
On Tuesday, they learned that six players will be on the ballot for fan voting for the starting lineups for the all-star game Jan.25 in Montreal, tied for most in the league with Detroit.
Tanguay and Koivu are among them, as well as Kovalev, Markov, defenceman Mike Komisarek and second-year goalie Carey Price, who joked that he would get his family to flood the NHL website with votes.
Koivu said it was a sign the team was being recognized as a contender.
"It's mainly because of the way we played last year - we had a lot of success and a lot of guys had good years," said Koivu. "This is where we want to be as a team, to have people saying we're going to finish first or second and we're going to go all the way, or go far in the playoffs.
"We look forward to the challenge. It would be amazing if we had a couple of guys on the (all-star) team."
Koivu was also asked if he would like a contract extension similar to the one signed last week by Ottawa Senators captain Daniel Alfredsson, so he could finish his career with the Canadiens, who drafted him in 1993.
"With the salary cap and with the way the market is, it's become rare to see a player play his whole career with one team," said Koivu, who can become an unrestricted free agent on July 1. "I'm very proud that I've been here all my career.
"You need both sides (to agree). The team has to have plans for me and I have to want to stay here. I can't say yes or no at this point, but it's something I've thought about and it would be a huge honour to finish my career with the Canadiens. But at this point, there haven't been any talks. I'm focused on what's happening on the ice and we all hope things work out."