Angela James scored four times in a game twice during her Hockey Hall of Fame career. Current national team assistant coach Danielle Goyette and Laura Schuler also scored four goals in a game during their career.
Poulin, from Beauceville, Que., was the first to accomplish the feat since 1994.
"For sure, it's exciting, but it's team play and those goals would not happen without my teammates," said Poulin.
The 22-year-old also scored both goals in Canada's 2-0 win over the United States to win Olympic gold in 2010.
Canada was minus captain Hayley Wickenheiser and assistant captain Caroline Ouellette for Wednesday's game. Both players were scratched from the lineup prior to the game with upper-body injuries and are said to be "day-to-day."
"They just weren't ready to go," head coach Dan Church said. "Whether it's one or two more days, they need to be 100 per cent to go.
"Hayley was a lot better today, but still probably wouldn't be able to go tonight and Carol just needed another day to do some rehab. Hopefully they'll both be back in the lineup for Friday, but we won't know that until probably Friday morning."
The defending champions opened the tournament with a 3-2 shootout win over the U.S on Tuesday. The absence of Wickenheiser, Canada's all-time leading scorer, and Ouellette forced Church to be creative with his line combinations.
Canada's forwards made the most of their extra ice time. Defenders Meaghan Mikkelson and Tessa Bonhomme played the odd shift at forward.
Brianne Jenner scored twice and Jennifer Wakefield had a goal and two assists. Mikkelson, Rebecca Johnston, Natalie Spooner, Sarah Vaillancourt and Haley Irwin also scored, with Jayna Hefford contributing a short-handed goal.
Charline Labonte stopped 16 shots for the shutout in front of 6,272 at SBP Arena.
"We just wanted to work on our systems and our habits and the things that are going to make us successful if we get to the medal round," Jenner said. "It's easy in games like that to lose focus and kind of move away from our game and maybe play a different style of hockey than we want to."
Poulin's third goal was awarded after a review. When she backhanded the puck upstairs on Swiss goalie Sophie Anthamatten, Poulin and Hefford raised their arms in celebration, only to watch play continue down the ice. Officials examined the play on the next whistle and awarded Poulin her third goal.
"I think when Jayna Hefford tells you it's a goal, I think you absolutely agree with that," Poulin said.
Canada topped Pool A with five points ahead of the U.S. with four points. Finland had three and the Swiss zero. The Americans doubled the Finns 4-2 on Wednesday. Canada concludes the preliminary round Friday against the Finns.
Russia downed the Czech Republic 3-1 to lead Pool B at 2-0. The Czechs were second at 1-1. Sweden downed Germany 3-2 in overtime to sit third at two points ahead of Germany with one.
The top two countries in Pool A get byes to the semifinals while the bottom two face the top two from Pool B in the quarter-finals. The bottom two teams in B fall to the relegation round.
Switzerland won bronze at last year's world championship in Burlington, Vt., for that country's first medal in tournament history.
Goaltender Florence Schelling can take much of the credit for that medal, but she did not play against Canada. The Swiss are saving her for games they need to win later in the tournament to preserve their ranking.
Anthamatten started strong in net and the Swiss attempted an aggressive forecheck. They were eventually worn down by Canada's superior size, speed, fitness and puck possession skills. Canada outshot the Swiss 79-16.
"We knew before they're stronger, they're faster and we said "we'll go shift by shift for 60 minutes," Swiss captain Julia Marty said. "Obviously you're disappointed if you give up 13 goals.
"The first 20 minutes went well. I've played Canada a couple of times and I thought we'd never played that well. Now that we can keep it up for 20 minutes, our next goal is to keep it up for 60 minutes."
Anthamatten, 21, was replaced by Dominique Slongo with less than four minutes remaining in the game.
It's the worst beating Canada has given the Swiss in five world championship meetings, but Church did not want his players taking their foot off the gas until the final buzzer.
"Are we supposed to try and aim for goalposts? We're not trying to embarrass them. We're trying to get better," Church said. "If we take a period off, I don't think it helps us and I don't think it helps the game.
"Should Usain Bolt ease up at the 50-metre mark? I don't know how you do that and become as good as you can. We want to be as good as we can and I don't think we should apologize for that."
Added Jenner: "We're here to defend our gold medal, really. We can't really worry about what people are going to say about our game too much."