First-half goals from Sarah Hunter and Bryleeh Henry cancelled out a stunning opener from Costa Rican captain Alexandra Pinell before Kirsty Fenton guaranteed victory with their third goal in the second half.
Costa Rica opened the scoring after 19 minutes when Pinell unleashed a rocket of a free kick from 35 yards out, delighting the 22,506 crowd.
The Young Matildas rallied and continued to test Costa Rica's defence and were rewarded for sustained pressure.
Captain Sheridan Gallagher's Gallagher's cross from the left was handballed by a Costa Rican defender and Sydney FC's Hunter stepped up to coolly slot home from the spot.
The Young Matildas then made it two in two minutes.
Gallagher's cross in from the right-hand side in the 72nd minute was too hot for goalkeeper Genesis Perez to handle.
Henry and player of the match Daniela Galic were waiting to pounce on the parry, but it was Henry who secured the last touch.
The Australians scored their clincher from a set piece. Hana Lowry's corner was sent perfectly into the hot spot and full back Fenton headed home from close range.
The Young Matildas now top Group A after Brazil and Spain shared the spoils in a scoreless draw.
Their coach Leah Blayney recorded a piece of history as the first Australian woman to coach at a FIFA tournament.
The Young Matildas next face Brazil, the U20 South American champions, on Sunday at 0600AEST.
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