Manager Luis Enrique made six changes as Les Parisiens looked to bounce back from Tuesday’s 2-1 UEFA Champions League defeat by Sporting CP.
They should have gone ahead inside two minutes when Barcola raced through on goal, but the forward delayed his shot, allowing Auxerre keeper Donovan Leon to make a sprawling block.
Khvicha Kvaratskhelia was then thwarted after eight minutes when his mazy run into the penalty area gave the forward a clear sight of goal, only for a last-ditch block to save the hosts.
Auxerre survived the early onslaught and grew into the contest, with their sights set firmly on narrowing the gap to safety that stood at six points heading into the weekend.
Leon remained a busy man, though, with the goalkeeper parrying away a towering header from PSG’s top goalscorer Goncalo Ramos and then blocking Ibrahim Mbaye’s low shot.
The visitors had scored a pre-round Ligue 1 high of 18 first-half goals this season, so Auxerre will have been delighted to reach the interval without conceding.
Barcola flashed a low shot past the post six minutes after the break, but Auxerre had chances of their own as Danny Namaso fired over from long range and top goalscorer Lassine Sinayoko curled an effort wide.
Enrique brought on Ballon d’Or winner Ousmane Dembele and Desire Doue just after the hour mark, before Barcola went close again when he lifted the ball onto the roof of the net from a tight angle.
Barcola had been PSG’s most dangerous player all night, so it was only fitting that he finally broke the deadlock 11 minutes from time, when the forward ran onto Dembele’s through ball and dinked the ball into the net via a touch from Leon. It was his seventh Ligue 1 goal of the season, and he has now lost only one game in which he has scored for Les Parisiens (W25, D2).
Auxerre hunted an equaliser, but PSG saw the game out to move two points above Lens at the summit having played a game more, while the hosts remain second-bottom after suffering a 14th defeat in 19 games across all competitions.
Flashscore Man of the Match: Bradley Barcola (Paris Saint-Germain)