Jerome Verrier scored twice and the host Remparts turned the tables on the Rimouski with a 5-2 victory in the tiebreaker game on Thursday night.
They will have less than 24 hours rest before they face the Western Hockey League champion Kelowna Rockets in the semifinal Friday night. It will be Quebec's third game in as many nights, while the Rockets will have had two days rest.
"It's the semifinal of the Memorial Cup so we're not nervous about energy," said Remparts goalie Zach Fucale. "We'll play hard and play our game.
"All year, every team plays three-in-three every two or three weeks. It's nothing we haven't faced before."
The winner plays the Ontario Hockey League champion Oshawa Generals (3-0) in the final on Sunday.
The Remparts beat Kelowna 4-3 in the opening game of the tournament, but they know it will be a tougher test now that the Rockets have adjusted to the time zone change and shook off the rust of a long layoff after winning the WHL title.
"I think we need to expect a better Kelowna team this time," said Fucale. "It was the first game for everyone. It'll be a great game."
Adam Erne, Anthony Duclair and Marc-Olivier Roy also scored for Quebec, which had lost its six previous meetings with Rimouski at the Pepsi Colisee including a 4-0 defeat on Wednesday night in round robin play at the four-team tournament.
Samuel Morin and Jeremy Lepine scored for Rimouski, which was eliminated.
The teams faced one another 19 times this season and the rivalry had bitter moments but the teams lined up and shook hands after the game.
"We're all sad and disappointed at the outcome, but if we take a breath and look at our season, we have something to be proud of," said Rimouski defenceman Simon Bourque.
A sparse crowd of 6,533 turned out as the teams met for the ninth time in 24 days, including the Quebec Major Junior Hockey League final won in Game 7 overtime by the Oceanic.
This time, the Remparts were on top of the Oceanic from the outset, checking hard and using their speed to draw penalties and keep pressure on the defence.
"The key was moving our feet," said defenceman Ryan Graves. "We're a fast team and teams have trouble skating with us."
On Wednesday night, the Oceanic dominated 4-0 and Quebec coach Philippe Boucher blasted the two QMJHL referees for bias against his team, for which he was fined $10,000.
With refs from Ontario and the West working the tiebreaker, the Remparts got the first three power plays and scored on the third one as Verrier, a 21-year-old undrafted forward, deflected Graves' point shot past Philippe Desrosiers at 17:19 of the first.
Morin tied it on a bullet, off-wing one-timer on a power play 2:32 into the second frame, but the Remparts answered at 3:58 when Duclair snapped a shot past Desrosiers off a drop pass from Kurt Etchegary.
Francois Beauchemin stripped the puck from Vladlimir Tkachev in the neutral zone and fed Lepine for a goal at 16:07, but again the Remparts answered right away as Desrosiers misplayed a clearing attempt and Erne scored from a scramble in the crease at 16:54.
Verrier went to the net to tip in Massimo Carozza's pass at 19:19.
Roy took a stretch pass at the far blue-line and tapped one in after a collision with Desrosiers at 11:31 of the third.
Fucale rebounded from being pulled the night before with a solid effort as Rimouski outshot Quebec 32-31.