Real Madrid forward Kylian Mbappe took his World Cup goals tally to 14, just two behind all-time leader Miroslav Klose, as Bradley Barcola also struck to help Les Bleus secure all three points for Didier Deschamps' side.
Mbappe darted across the penalty area to convert a brilliant Michael Olise pass on 66 minutes and break the deadlock in a contest in which France struggled in the first half before coming to life after the break. France's Kylian Mbappe celebrates after scoring thrid goal during the World Cup Group I soccer match between France and Senegal.
Barcola of Paris Saint-Germain then came off the bench to add the second late on, before his club colleague Ibrahim Mbaye pulled one back in stoppage time for Senegal.
Mbappe had the final word, blasting in from long range in the 96th minute to seal the win and become France's all-time top scorer with 58 goals.
Fearsome France begin World Cup wary of over-confidence
Mbappe makes history
The decision by Deschamps to move Olise infield from the right wing was crucial in swinging the game in favour of the two-time world champions.
But it was Mbappe who grabbed the spotlight in what proved a memorable 99th appearance for his country.
The 27-year-old renewed his extraordinary World Cup record, having scored in the 2018 final as France lifted the trophy and netted a hat-trick in their penalty defeat to Argentina in the 2022 final in Qatar.
His double took him past Pele's tally of 12 and beyond the 13 of Lionel Messi and fellow Frenchman Just Fontaine. He is now level with Gerd Mueller, with only Klose and Brazilian Ronaldo, on 15, ahead of him.
France, one of the pre-tournament favourites, will be expected to build on this result as they look to advance from the group stage, with outsiders Iraq next up before a meeting with Erling Haaland's Norway.
Deschamps, approaching his final tournament before stepping down after 14 years in charge, has been wary of overconfidence in his talented squad.
Senegal served as a reminder of what can go wrong. France entered the 2002 World Cup as holders and favourites, only to lose 1-0 to the Lions of Teranga in the opening game and exit in the group stage without scoring.
Deschamps tips hat-trick man Olise to make big impact at World Cup
Olise turns the tide
Senegal demonstrated their quality before a packed house of 80,545, with the Manhattan skyline visible in bright sunshine beyond the stadium.
A side led by veteran forward Sadio Mane, and featuring four starters born in France, were playing their first competitive match since winning the Africa Cup of Nations final in Morocco in January, a title they were subsequently stripped of following a walk-off protest by several players during the match, with their appeal still ongoing.
Senegal were the better side in the first half. Nicolas Jackson almost broke the deadlock on 25 minutes, breaking away and hitting the post before the ball came back off goalkeeper Mike Maignan and went just wide. Ismaila Sarr then put a glorious chance over the bar in stoppage time, and Senegal would come to regret both misses.
Africa's finest: Senegal, runners-up with something to prove
Deschamps responded at the interval, switching Olise and Ousmane Dembele, with the reigning Ballon d'Or winner moving to the right and vacating the central area behind Mbappe for the Bayern Munich man.
France came to life immediately. Olise was denied by Edouard Mendy before setting up Mbappe for a chance that was saved. France felt they had a penalty on the hour when Mbappe went down under a Mane challenge, but referee Alireza Faghani declined to award a spot-kick after a review.
It mattered little. Olise continued to cause problems and slipped in Mbappe for the opener, a superb finish that settled French nerves. Adrien Rabiot then released substitute Barcola to run through and make it two.
Mbaye reduced the deficit on 95 minutes, but Mbappe ensured there would be no late drama.
(with newswires)


FBI foils plot to attack White House UFC event using explosive drones, snipers
How 17-year-old Mfantsipim SHS final-year student committed suicide
Ashaiman Police arrest two suspects over series of armed robberies
Abort all pending US extradition requests until Ken Ofori-Atta returns – Ras Mub...
Interior Ministry lifts motorbike ban in Binduri after security improves
Thomas Partey to miss Ghana’s World Cup opener after Canadian court dismisses vi...
Ghana boss Queiroz hails spirit of players ahead of Panama clash at World Cup
Ken Agyapong has the appeal young voters who don’t believe politicians will grav...
Nobody has the right to close part of public hospital without my consent – Healt...
Russian warship fires warning shots at UK-flagged yacht in the English Channel