Mbappe converted from the spot in first-half stoppage time after the referee awarded a penalty for handball on a VAR review, restoring PSG's lead following Neymar's early opener and a Duje Caleta-Car equaliser.
PSG are 15 points clear of second-placed Marseille with six games remaining and Mauricio Pochettino's side -- who also have a far superior goal difference -- stand poised to reclaim the trophy they relinquished to Lille last season.
If Marseille fail to beat Nantes on Wednesday then PSG will officially secure their eighth Ligue 1 title in 10 seasons if they can better their nearest rivals' result when they face Angers.
Despite the apparently high stakes for the biggest fixture in French football, there was a distinctly flat atmosphere at the Parc des Princes.
Authorities banned Marseille fans from the game over concerns of possible violence, a recurring them in France in recent months.
Meanwhile, PSG 'ultras', the most vocal members of their support, have decided to stay silent until the end of the season in protest at the club's management and at results in a campaign marked by the Champions League last-16 exit to Real Madrid.
In any case, a record-equalling 10th French championship in their history has never really been in doubt for PSG, even before their current run of three straight wins in which Neymar and Mbappe have each scored six times.
The Brazilian gave PSG a 12th-minute lead, meeting a flighted ball forward by Marco Verratti and lobbing stranded goalkeeper Pau Lopez.
Marseille drew level just after the half-hour as Gianluigi Donnarumma made a mess of dealing with a corner, allowing Caleta-Car to prod home on the line.
Lopez saved a Neymar free-kick and Messi had two goals disallowed for offside before PSG were awarded the penalty deep in stoppage time at the end of the half.
Valentin Rongier blocked a shot with his thigh, the ball ricocheting up and striking his elbow, an infringement spotted by the referee after he was invited over to the pitchside monitor.
Mbappe's successful penalty was his 21st Ligue 1 goal of the season and 32nd in all competitions.
