Gauthier scored two and had two assists for the Oceanic (10-1-1), who pulled away with five unanswered goals.
Anthony DeLuca, Peter Trainor, Simon Bourque, Michael Joly and Beau Rusk added singles for Rimouski, while Alex St-Pierre made 28 saves in net.
Jean-Francois Plante had the lone goal for the Phoenix (3-9-2), and Gabriel Parent allowed all seven goals on 22 shots.
DRAKKAR 7 TIGRES 0
At Victoriaville, Que., seven players each scored as Baie-Comeau crushed the Tigres.
Frederic Gamelin, Nicolas Meloche, Denis Gorbunov, Bokondji Imama, Dominic Poulin, Gabriel Verpaelst and Valentin Zykov had singles for the Drakkar (9-4-2).
Philippe Cadorette made 22 saves in net for Baie-Comeau. At the other end, Brandon Whitney and Steven Veilleux combined to stop 24 shots for Victoriaville (8-4-1).
The power play was tough on the Tigres at both ends of the ice — they went scoreless in six opportunities, while allowing the Drakkar to score three on 10 attempts.
ISLANDERS 3 SAGUENEENS 0
At Charlottetown, Eric Brassard made 34 saves to help the Islanders shut out Chicoutimi.
Brassard was especially good in the third period, when the Islanders were outshot 17-11.
Matej Beran, Anthony Cortese and Bradley Kennedy each scored for Charlottetown (10-2-1).
Domenic Graham stopped 40 shots for the Sagueneens (7-8-0).
HUSKIES 5 MOOSEHEADS 3
At Halifax, Maxime St-Cyr scored twice to put Rouyn-Noranda ahead for good.
Jean-Sebastien Dea, Marcus Power and Justin Guenette also scored for the Huskies (7-4-2).
Darcy Ashley scored twice for the Mooseheads (9-7-0), and Max Lindsay also had a single.
Rouyn-Noranda goaltender Carl Hozjan made 35 saves, while Kevin Darveau stopped 16 shots for Halifax.
REMPARTS 5 SEA DOGS 2
At Saint John, N.B., Callum Booth made 35 saves and got lots of help from Quebec's offence for the win.
Fabrice Herzog, Jason Houde, Adam Erne, Kurt Etchegary and Anthony Duclair scored for the Remparts (6-5-3).
Spencer Smallman and Jason Cameron replied for the Sea Dogs (5-7-1).
Sebastien Auger stopped 23 shots for Saint John.
OLYMPIQUES 3 ARMADA 1
At Gatineau, Que., the Olympiques stifled the league-leading Armada's offence.
Robert Steeves needed to make just 12 saves for Gatineau (9-5-0), while Vincent Dunn, Emile Poirier and Vaclav Karabacek each scored.
Philippe Sanche had the only goal for Blainville-Boisbriand (10-1-1), and Etienne Marcoux stopped 19 shots.
Neither team recorded double-digit shots in any period, and the Armada were held to just three shots in the third.