World Cup winner Mbappe, back from a three-match ban following 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 their 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 1965-66.
1966 - Kylian Mbappé est désormais le 1er joueur français à inscrire au moins 32 buts sur une saison en Ligue 1 depuis Philippe Gondet avec Nantes en 1965/66 (36). Update. https://t.co/8BUbTJft5P— OptaJean (@OptaJean) May 18, 2019
PSG's form since being confirmed as champions had been patchy, and their win over Angers last time out was just their second in seven Ligue 1 games, but their rapid start ensured they could coast to three points at the 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.
What does it mean? Mbappe's individual haul the aim now
Having lifted the league title after the game, PSG have very few collective goals remaining – though they would become the first team in the 20-club Ligue 1 era to score in every fixture if they find the net at Reims next week. Instead the focus is on Mbappe's duel with Messi to become the most potent striker across Europe. With his brace here, the young star certainly gave himself a chance to beat the man many consider the greatest ever.
Mbappe back with a bang in Neymar's absence
Mbappe might be closer to Messi had he not served a three-match ban following his dismissal against Rennes last month. But he showed no sign of any rust with a poacher's goal prior to the break and a delicious finish in the second half. Neymar took the plaudits in the win over Angers last time out but Mbappe's display here meant the Brazilian was not missed.
Dijon not cutting the mustard
Considering their Ligue 1 status is hanging by a thread, Dijon put up no fight whatsoever and this game was over as soon as Di Maria and Cavani scored early on. For that effort, head coach Antoine Kombouare deserves to be criticised.
Barcelona play their final league fixture on Sunday, which means Mbappe will know how many goals he needs to pip Messi by the time PSG travel to Reims on Friday. Dijon, two points behind 18th-placed Caen, who are in the relegation play-off place, will know even a victory against Toulouse may not save them.