Topping Group C in the process, La Albiceleste secured the triumph thanks to goals from both Brighton's Alexis Mac Allister and Manchester City forward Julian Alvarez.
PSG star Lionel Messi squandered a golden opportunity from the penalty spot in the first half, with Wojciech Szczesny denying him from twelve yards.
Argentina topped the group on six points, with Poland also progressing to the knockout stages ahead of Mexico, despite finishing level on the same points and losing to Licha's nation at Stadium 974 this evening.
Despite Martinez not featuring across the 90 minutes in Doha, Argentina were largely in control throughout proceedings, with Alvarez first testing Szczesny early on.