Mbappe scored a penalty in the 81st minute and a beautiful volley 97 seconds later to help France come back from two goals behind in regular time and attempt to become only the third team in history to win the trophy again.
In the 108th minute, Angel Di Maria restored the lead for the Albiceleste after Messi had given his team the early advantage.
However, Mbappe responded once more two minutes before the end of extra time.
This set up penalties, which Messi and Mbappe both converted before Argentina bid their captain farewell to the World Cup.
A bright Argentina start was rewarded when Messi calmly beat Hugo Lloris from the penalty spot in the 21st minute after Ousmane Dembele made contact on Di Maria in the box.
Messi’s flicked pass into the path of Julian Alvarez, who in turn played in Alexis Mac Allister to find Di Maria on the far side, was sublime.
But Didier Deschamps made a double substitution before halftime, bringing in Marcus Thuram and Randal Kolo Muani, and both players made an immediate impact.
After toiling for much of the second half, France was awarded a penalty, which Mbappe converted after Nicolas Otamendi dragged down Kolo Muani.
Mbappe, who had been a peripheral figure until that point, then stepped up moments later with a powerful volley from Thuram’s pass.
Messi appeared to have won it for Argentina in extra time after reacting quickest to a saved Lautaro Martinez attempt, only for Paris Saint-Germain teammate Mbappe to equalize through a penalty after his shot hit Montiel on the arm.
Montiel, with the assistance of Martinez, would have the final say as Messi and Argentina ended their wait.
This was a fitting conclusion to a World Cup that saw a record 172 goals scored, surpassing the 171 netted in the 1998 and 2014 editions.
The game appeared all but over with 10 minutes to go as France, who became the first team on record not to attempt a first-half shot in a World Cup final, struggled to get going.
The term “responsibility” refers to the act of determining whether or not a person is responsible for his or her own actions.
Mbappe scored his three goals from six shots, joining England’s 1966 World Cup hero Geoff Hurst as the only players to ever score a hat-trick in a World Cup final.
Although it won’t be much comfort to the PSG star, he ends the competition with eight goals, one more than Messi.
Messi may have been almost completely eclipsed by Mbappe on an individual level, but he still contributed significantly to both this victory and Argentina’s tournament success.
He became the first player to score in each round of the competition while making a record-breaking 26th and final appearance on the biggest stage of them all.
His 21 goal involvements are also the most of any player in World Cup history.