Mbappe’s goals, his 27th and 28th of the season in Ligue 1, both came in the first eight minutes at the Stade Abbe-Deschamps and set PSG up for victory.
Auxerre pulled one back early in the second half through Lassine Sinayoko but Paris held on for a victory which leaves them six points clear of second-placed Lens with two games remaining.
They require just a draw away to Strasbourg next weekend to officially be crowned champions for a French record 11th time.
However, a goal difference advantage of 16 over Lens means they are almost certain to win the title even if they end the season level on points with their rivals.
Mbappe opened the scoring in style, collecting a Fabian Ruiz pass and turning home defender Gauthier Hein inside out before shooting high into the net.
It was 2-0 two minutes later, as Hugo Ekitike left a Lionel Messi pass for Mbappe to rifle in a shot from the edge of the area.
Rayan Raveloson hit the bar late in the first half for the hosts, who reduced the deficit six minutes after the break when Nuno da Costa headed on a long clearance downfield for Sinayoko to run through and score.
Christophe Galtier’s PSG team had hoped to celebrate winning the league on Sunday, but a 3-1 victory for Lens in Lorient earlier ensured they would have to wait at least another week regardless of their result in Auxerre.
The result left Auxerre still one point and one place above the relegation zone with two matches of the season to play. (AFP)