Anderson took over from late-season hero Andrew Hammond in Game 3 and has posted an overtime loss and two wins.
Montreal, with a 3-2 lead in the best-of-seven series, gets a third chance to end it in Game 6 on Sunday night at the Canadian Tire Centre.
Anderson has saved 120 of 123 shots in three games, including 45 of 46 in Ottawa's 5-1 win in Game 5 at the Bell Centre. His play is reminiscent of 2013, when the Senators upset Montreal in five games in the first round.
But Montreal forward Dale Weise says the Senators veteran has not crept in the Montreal shooters' minds.
"We're not a team that scores that much, so goalies can't get in our heads," Weise said Saturday. "Really, that's the answer.
"Goalies don't rattle us too much. Every goalie's had our number all year. When we get 46 shots, I like our chances. Keep getting there, take his eyes away, get some rebounds. It's going to happen for us."
The Canadiens scored 221 goals in 82 regular-season games, tied with Pittsburgh for the lowest total among teams that made the playoffs.
Backstopped by Vezina Trophy candidate Carey Price in their own net, and not many snipers up front, the Canadiens finished first in the Atlantic Division by winning a lot of low-scoring games.
But to prevent the series from going to a nervy seventh game and eliminate the possibility of becoming only the fifth NHL team to lose after leading a series a 3-0, they'll need to find a way to get through the Senators aggressive checking and big defence and get pucks past Anderson.
"We're up 3-2. We're a confident group. We're comfortable playing on the road. There's no reason for us to be frustrated," said Weise, whose overtime goal secured a 2-1 win against Anderson in Game 3.
The Senators have been especially good at stifling Montreal's power play, which is 1 for 19 in the playoffs. They've been especially good at limiting clear shots from the power-play's main motors, point men P.K. Subban and Andrei Markov.
The Canadiens top scorer, left-winger Max Pacioretty, had the Canadiens' only man-advantage goal in Game 2.
"They blocked a lot of shots, they know our tendencies, so it comes down to getting outside our comfort zone and trying new stuff," Pacioretty said of the power play. "Everyone's got to be shooters and passers.
"We can't be predictable. They're covering the points well so we have to get the puck to the guy on the half wall and make some low plays. We haven't done it too much, but once you do it, they'll start respecting that and open up the top as well."
Coach Michel Therrien may shuffle his top lines to try to get some struggling forwards going as well.
The Canadiens' trouble with Anderson boiled over late in Game 5 when Brandon Prust drifted into his crease and was given a poke in the ribs. Prust speared Anderson in the mid-section and the goalie gave him a couple of whacks with his stick before it ended in a mass shoving and wrestling match.
Prust has not been available to comment on the incident, but Therrien did.
"We have to make life a lot more difficult for Anderson," he said. "Throw a lot more pucks at the net.
"He's having great playoffs. Give him credit for that. But in that case, he poked our player in the ribs. He's a guy who uses his stick to hit guys in front of the net. But this time he picked the wrong guy."
Price had little chance on Ottawa's first three goals and remains the team's best hope to advance to the second round. His teammates count on it.
As centre David Desharnais put it: "With all due respect, we have more confidence in our goaltender than they do in theirs."