Chhetri struck a brace against Bangladesh in the FIFA World Cup qualifiers match in Qatar.
Chhetri, who scored his 73rd and 74th international goals, is second behind Portugal’s Cristiano Ronaldo, who has 103 international goals.
The 36-year-old is now placed 11th on the all-time goal-scorers list in men’s international football.
United Arab Emirates’ Mabkhout took his tally to 73 after his goals against Malaysia last week, while Argentina’s Messi scored his 72nd international goal against Chile last Thursday.
Mabkhout will have an opportunity to regain the second spot when UAE takes on Thailand, Indonesia and Vietnam next week. Chhetri, too, could extend his lead when India faces Afghanistan on June 15.
Messi will be in action during the Copa America, which begins on June 13 in Brazil.