Veteran forward Girelli’s 54th international goal was enough to settle the bruising Group G encounter in front of 30,889 fans at Auckland’s Eden Park on Monday night.
Six yellow cards were handed out in the feisty affair – the most of any match at the tournament so far.
Girelli, the oldest member of Italy’s squad, was brought on as a substitute in place of Giulia Dragoni, the youngest, and needed just four minutes to find the net.
The 33-year-old rose highest to meet Lisa Boattin’s cross and nodded home the winner in the 87th minute, sparking wild scenes.
“There’s nothing special, it’s just that I did my duty,” Girelli said to reporters.
“I did my best. I was really willing to help my teammates.”
Argentina had a late chance to equalise, but Florencia Bonsegundo’s free kick from the edge of the box in stoppage time was brilliantly saved by Francesca Durante.
Italy finished winless at the bottom of their group at last year’s Euros but have already bettered that performance at the World Cup.
“In the end the girls deserved the victory,” Italy coach Milena Bertolini said, adding that Girelli brings “added value” to the team.
“She is a captain and she is always there.
“When she comes in she does what she knows how to do and she does it very well, as do the others.
“Now we will enjoy this victory, then we will start working to prepare for the next game [against Sweden on Saturday].”
The result left Argentina still searching for their first World Cup victory after 10 matches across four tournaments.
Argentina face South Africa on Friday, with Italy and the highly-ranked Sweden set to clash the following day.
Italy were the more threatening side throughout Monday night’s contest and twice put the ball into Argentina’s net before halftime, only for scores to remain level.
The strikes by Arianna Caruso and Valentina Giacinti were swiftly and correctly ruled out for offside.
Caruso’s was a neat, curling effort that served as a warning shot inside 15 minutes.
Argentina’s best chance of the first half was a speculative and acrobatic attempt by experienced forward Mariana Larroquette, which flashed wide in the opening minute.
Larroquette was in the thick of the action and received an early yellow card for a two-footed challenge on Barbara Bonansea.
Fouls came thick and fast in a physical contest, and Caruso was booked for holding back Larroquette after losing possession to her opponent.
Argentina’s Miriam Mayorga and Bonsegundo were both booked after the break, for hauling down Bonansea and Sofia Cantore respectively.
Bonansea and Argentina’s Eliana Stabile were also shown yellow cards late on as tempers flared.
Argentina caused plenty of issues for Durante in the Italian goal with balls into the penalty area, but couldn’t manage a shot on target until Bonsegundo’s free kick in the 94th minute.
Dragoni became her nation’s youngest ever World Cup player at 16 years and 259 days.
AAP