Tobias Badila's own goal and strikes by Bernardo Silva and Thomas Lemar put the principality side on 86 points with three games to play, while PSG, who have two games left, crushed Bastia 5-0.
Monaco, who have a much better goal difference, will be virtually champions if they beat Lille at home next weekend.
Leonardo Jardim's side went ahead after three minutes when Badila deflected Valere Germain's cross into his own net.
Portugal midfielder Silva headed home from Lemar's cross to make it 2-0 five minutes before the break.
Lemar sealed a straightforward win four minutes from time, after latching on a Kylian Mbappe pass.
Earlier, PSG had kept alive their own slim title hopes.
There was a minute of applause before kickoff to mark the 25th anniversary of the Furiani tragedy that killed 18 people in 1992 when one of the terraces of the stadium collapsed before a French Cup semi-final.
PSG went ahead in the 32nd minute when Lucas latched on to a cross from Blaise Matuidi.
Marco Verratti doubled the tally three minutes later with a 25-metre effort while Bastia keeper Jean-Louis Leca was tending to the apparently injured Matuidi.
Edinson Cavani increased the lead when he tapped in from Goncalo Guedes's cross in the 76th minute.
Marquinhos made it 4-0 six minutes later, pushing the ball into the net after Giovani Lo Celso had beaten Leca with a delicate chip, just after Cavani had missed a penalty.
The Uruguay striker made up for his miss one minute from time with his 33rd league goal of the season.
(Reporting by Julien Pretot; Editing by Clare Fallon)
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