Martinez, 27, smashed home a left-footed volley from Lionel Messi's cross after 55 minutes for his 32nd international goal on his 70th appearance.
The Inter Milan captain now sits joint-fifth alongside Argentina legend Maradona, though he remains some way behind top-scorer Messi's 112 goals.
Gabriel Batistuta, Sergio Aguero and Hernan Crespo complete the top five.
Inter Miami forward Messi, 37, is now tied with former United States forward Landon Donovan for most international assists with 58.
Lionel Scaloni's side were on top for much of the game but were unable to extend their lead, with Julian Alvarez hitting the post and Liverpool's Alexis Mac Allister sending a header wide
The win moves Argentina five points clear at the top of the South American World Cup qualifying table with six games remaining.
Elsewhere, Brazil were jeered by their own fans as they drew 1-1 against Uruguay in Salvador.
Real Madrid midfielder Federico Valverde put Uruguay in front early in the second half, but Gerson levelled for Brazil six minutes later with his first international goal.
The draw means five-time World Cup winners Brazil sit fifth in the table, with the top six qualifying automatically for the 2026 tournament in United States, Canada and Mexico.
A fine solo goal from former West Ham and Everton forward Enner Valencia secured a 1-0 win for Ecuador away at Colombia, moving them above their opponents into third on goal difference.