Biereth controlled Caio Henrique's pass on his chest and guided the ball home in the 77th minute on Saturday (Sunday EDT) for his 11th league goal in 11 games since joining from Austrian side Sturm Graz in January.
Midfielder Maghnes Akliouche struck with a late penalty for Monaco, who overtook fourth-placed Nice on goal difference with eight rounds left after this weekend's games.
The Riviera rivals meet in the next round on March 29, with the top four earning a place in the Champions League next season.
After being eliminated from the last 16 of the Champions League in midweek, fifth-placed Lille lost 1-0 at Nantes despite having an extra player for the closing stages.
The defeat could prove costly in the race for a Champions League spot, because Lille would drop to sixth if Lyon beat struggling Le Havre at home on Sunday.
Nantes hit the crossbar three times before having defender Jean-Charles Castelletto sent off in the 74th minute for fouling forward Chuba Akpom.
Persistence paid off when Mostafa Mohamed headed in Moses Simon's cross in the 83rd minute.
The win means Antoine Kombouare's Nantes side move clear of the relegation zone and into 13th place.
Wesley Said scored the only goal of the game as Lens beat Rennes 1-0 to consolidate their hold on eighth place.
Said started his career at Rennes, coming through the reserves and playing four seasons with the first team before leaving in 2017.
He netted with a header at the near post following a corner in the 47th minute.
The loss left inconsistent Rennes in 12th spot.
On Sunday, unbeaten PSG could move closer to another title with a home win against bitter rivals Marseille.
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