After a goalless first half, Mbappe opened scoring in the 66th minute before substitute Bradley Barcola doubled the lead with eight minutes of regulation time still remaining.
Senegal pulled a goal back through Ibrahim Mbaye but Mbappe killed off any hopes of a comeback with a brilliant long-range effort deep into stoppage-time.
The French superstar now has 58 goals for his country, one clear of Olivier Giroud, who held the record since December 2022.
Lions of Teranga were left to rue a few missed opportunities, especially in the first half, that could have changed the complexion of the contest.
Nicolas Jackson hitting the post while Ismaila Sarr inexplicably blazed an effort over the crossbar from point-blank range just before the halftime whistle.
France though showed why they came into the global tournament as one of the hot favourites when Michael Olise put in a brilliant through ball for Mbappe to finish just after the hour mark.
Barcola then showed the depth in the France squad when the forward came off the bench and showed a deft finish to beat Senegal shot-stopper Edouard Mendy.
The African country never gave up the fight and Mbaye produced an excellent finish to beat France goalkeeper Mike Maignan as Senegal sniffed they might still get a point.
The result was truly put to bed by Mbappe however as the striker made sure his team would take three points with an emphatic finish to the contest.
France next face Iraq on Monday while Senegal will look to get their World Cup campaign back on track when they take on Norway on Tuesday.