Mbappe had 14 touches in the scoreless first 45 minutes plus added time on Tuesday (Wednesday AEST), the fewest of any player, then showed his brilliance when he put Les Bleus ahead in the 66th minute. After Jules Kounde and Michael Olise twice exchanged passes on the right flank, Olise made a diagonal pass as Mbappe burst past Senegal captain Kalidou Koulibaly.
Playing at a third World Cup, 27-year-old Mbappe turned onto the ball just outside the six-yard box and slid it past Edouard Mendy and inside the far post in New Jersey.
Barcola entered in the 80th and scored two minutes later when he ran onto a through ball from Adrien Rabiot, took a touch and lifted the ball over Mendy for his fourth international goal.
Ibrahim Mbaye scored on an angled shot for Senegal five minutes into added time, but Mbappe netted a spectacular long-range goal a minute later, over Mendy's outstretched arm and just under the crossbar.
Mbappe moved one ahead of Messi and Just Fontaine on the World Cup career scoring list and is tied with Gerd Mueller, trailing only Brazil's Ronaldo (15) and Germany's Miroslav Klose (16). Mbappe also set a French record with 58 international goals, one more than Olivier Giroud.
Mbappe travelled to North America off the back of scoring 25 goals last season at club level for Real Madrid.
Trying to reach their third straight World Cup final, France play Iraq on Monday (Tuesday AEST) in Philadelphia, then close Group I against Norway in Massachusetts. Senegal meet Norway on Monday at the New York New Jersey Stadium and finish the first round against Iraq at Toronto.
