Messi, 35, overtook Gabriel Batistuta's previous record of 10 goals, which he scored at the 1994, 1998 and 2002 World Cups.
Messi put Argentina ahead in the 34th minute from the penalty spot following a foul on Julian Alvarez by Croatia goalkeeper Dominik Livakovic.
Messi's 11 goals also tie him for sixth for most goals in the history of the men's World Cup, with Sandor Kocsis and Jürgen Klinsmann. Only Miroslav Klose (16), Brazil's Ronaldo (15), Gerd Muller (14), Just Fontaine (13) and Pele (12) are now ahead of him.
He then equalled Batistuta's mark of 10 when he scored from the penalty spot in his side's fiery quarterfinal encounter with the Netherlands, which Argentina eventually won on penalties after a stirring Dutch fightback for a 2-2 draw.
In the match against Croatia, Messi also tied the record for most appearances at the World Cup when he played for the 25th time for Argentina at soccer's biggest tournament.
Messi's first World Cup goal came on his debut in 2006, as he scored after being substituted on to help his side to a 6-0 victory over Serbia and Montenegro.
Four years later, Messi failed to score in the entirety of the World Cup tournament in South Africa as an Argentina side managed by Maradona reached the quarterfinals but lost 4-0 against Germany.
The forward enjoyed a more fruitful 2014 tournament, scoring four times in Argentina's first three games as he helped them to the final -- where they were again beaten by Germany.
Messi scored just once at the 2018 World Cup but has netted four times in his side's five matches at the tournament in Qatar this year.
Messi is Argentina's all-time top scorer with 94 goals in 169 appearances for the national team since making his debut in 2005. Batistuta scored 54 times in 78 matches for Argentina.