FIFA World Cup winner Mbappe, back from a three-match ban after his red card in the Coupe de France final, scored in either half to move onto 32 goals for the season, two adrift of Barcelona striker Messi's haul of 34 in LaLiga, ahead of their respective teams' final fixtures.
PSG passed the 90-point barrier in its final home fixture of the campaign, Angel Di Maria and Edinson Cavani both netting inside the opening four minutes.
Mbappe then struck either side of the interval to become the first Frenchman to score 32 league goals in a Ligue 1 season since Philippe Gondet did so for Nantes in 1965/1966.
PSG's form since being confirmed as champion had been patchy, and it win over Angers last time out was only its second in seven Ligue 1 games, but its rapid start ensured it could coast to three points at Parc des Princes.
Di Maria's third-minute effort deflected off Wesley Lautoa to leave Dijon goalkeeper Runar Alex Runarsson stranded as the ball hit the net.
The goalscorer then turned provider a minute later, crossing the ball to the back post for Cavani to head in from close range.
Teenager Loic Mbe Soh was denied a first senior goal by the post when he nodded Thomas Meunier's cross against the woodwork before Mbappe stabbed in his first from virtually on the line after Cavani had almost turned in Layvin Kurzawa's cross.
Nine minutes after half-time, Mbappe displayed his ruthless streak again, racing onto Leandro Paredes' throughball and dinking over Runarsson to make it 4-0.
On an otherwise flawless night, the 20-year-old then squandered a chance to score his hat-trick, heading wide from a corner when unmarked before Runarsson denied him again late on.