Argentina beat Italy 3-0 in the final on Wednesday – a game between Europe and South America champions.
Messi provided two assists in that game and was again in the old form.
He opened the scoring with a penalty, and his fourth took him above Ferenc Puskas, who scored 84 goals for Hungary.
Messi is now the fourth-highest scorer in men’s international football behind only Malaysia’s Mokhtar Dahari (89), Iran’s Ali Dei (109) and Portugal’s Cristiano Ronaldo (117).
This is the first time the 34-year-old has scored five runs in a game. He has achieved the feat only once in his career, in a 7-1 victory for Barcelona over Bayer Leverkusen in the 2012 Champions League.
He would still have been close to Ronaldo, but the Portuguese scored twice in his country’s Nations League win against Switzerland on Sunday.
Messi’s goals in Pamplona showed his immense skill.
He put Lionel Scoloni’s team ahead with an excellent penalty after eight minutes, then doubled the lead in the roof of the net from a tight angle with a powerful side-footed effort.
His third performance was a hunter finish, showing his trademark accuracy to direct Nahuel Molina’s right-wing cross from 12 yards into the bottom corner.
His fourth was much due to his alertness. As the other players stopped and hoped for a free-kick prize that never came, Messi picked up a loose ball, drove it into the box, produced a dummy that left the Estonia keeper and a defender on the ground and hit the ball. Rolled in an empty net.
He concluded his remarkable performance when he was again the fastest to react to a loose ball and slipped into a low finish next to the penalty spot with 14 minutes to go.
While Estonia did not provide the most rigorous test, this result – combined with a win over Italy, their unbeaten World Cup qualifying campaign and last year’s Copa America victory – suggests that Messi may have a greater chance of winning the World Cup. Maybe, a trophy that has taken him out of his illustrious career.