Jessica Appiah converted the decisive spot-kick to send Ghana into the last eight after a dramatic encounter in which the West Africans played the closing stages with 10 players.
Ghana made a bright start and took the lead through Appiah, who finished from close range after being set up by Cynthia Obinsrewuo.
Argentina threatened an equaliser, with Mercedes Diz coming close after finding herself through on goal, only for her effort to clip the crossbar.
Obinsrewuo later appeared to have doubled Ghana’s advantage after chasing a long ball and lifting it over goalkeeper Bianca Virga, but the goal was ruled out for offside.
The Black Maidens’ task became more difficult when Hajara Adam was sent off after receiving a second yellow card with 13 minutes remaining.
Argentina capitalised on their numerical advantage as Diz met a looping free-kick with a powerful header that went over Ghana goalkeeper Belinda Marku Aklie to level the score.
Neither side could find a winner in regulation time, sending the contest to a penalty shootout.
Ghana held their nerve from the spot, with Appiah, Juliana Gyekyewaa, Rafia Osman, Christiana Ashiaku and Saraphina Essenam all converting their penalties.
Argentina’s Oriana Gomez missed her attempt, allowing Appiah to step up and score the decisive kick as Ghana won the shootout 5-4 to secure their place in the quarter-finals.
Ghana will now turn their attention to the quarter-final against either Kenya or Japan as they seek to continue their run in the tournament.
