Cape Verde came within a whisker of the greatest shock in World Cup history before Argentina finally shut the door 3-2 in extra time in a thrilling Round of 32 encounter at the Hard Rock Stadium in Miami.
The debutants matched the world champions blow for blow across 120 breathless minutes.
Lionel Messi struck early in the second half to break the deadlock, latching onto a long ball from Lisandro Martínez before finishing at the near post. It was his 20th World Cup goal and made him the first player to score in eight consecutive tournament appearances.
Cape Verde refused to fold. Deroy Duarte, on the eve of his 27th birthday, levelled midway through the second half, slipping the ball through Martinez's legs and past Emiliano Martinez to send the match to extra time.
Lisandro, fresh from his assist, restored Argentina's lead early in extra time. He finished from Nahuel Molina's flick-on after Messi had whipped in the initial corner, beating goalkeeper Vozinha at his near post.
Cape Verde struck back within 10 minutes through a moment of individual brilliance. Sidny Lopes Cabral cut inside from the left and curled a stunning effort into the top corner from 18 yards, a contender for goal of the tournament.
The Blue Sharks goalkeeper Vozinha, 40, then denied Messi twice more as the match ticked into the second period of extra time. His save tally for the tournament rose to 17, second only to Eloy Room and Orlando Gill.
Argentina finally found a winner in the 111th minute. Messi curled a corner to the edge of the six-yard box, where Cristian Romero rose highest to head goalwards. The ball took a deflection off Diney Borges and looped past Vozinha, later confirmed as an own goal.
Cape Verde pushed for a third equaliser in the closing stages but could not find a way through. Gilson Benchimol's header and Dailon Livramento's follow-up both went close without troubling the scoreline further.
Argentina's progress extends a curious tournament record. It was their 12th extra-time match in World Cup history, level with Germany for the most by any nation.
For Cape Verde, the defeat ends a remarkable run that began with three draws and no losses in the group stage. Ranked 67th in the world before the tournament, they were given little chance against the top-ranked Argentines.
Manager Bubista's side will nonetheless leave Miami as one of the stories of the tournament, their resilience and quality earning admirers well beyond their own supporters.
Argentina, meanwhile, advance to the last 16 with questions still to answer.