Messi joins a select club comprising only Juan Andres Marvezy and Manuel Moreno to score five in a game for Argentina.
The seven-time Ballon d’Or scored from the spot in the eighth minute, then added four more in the space of half an hour (45, 47, 71 and 76 minutes).
His quintet extended his record tally of goals for his country to 86.
Lionel Scaloni’s side are unbeaten in 33 matches, the last loss a 2-0 defeat to Brazil in the semi-finals of the 2019 Copa America.
At the World Cup finals in Qatar later this year Argentina are drawn with Saudi Arabia, Mexico and Poland.