The Australian showed remarkable grit to win the second set 6-4 to force a third and deciding set, after losing the opening stanza 7-5.
But it was then the turn of the American to rally hard, taking the final set 7-6 (7-5) to advance to the round of 64.
Little separated the two throughout the match. Both battled with serve with Pera committing 12 double faults to Saville's 13.
Pera converted nine out of 22 break-point opportunities while Saville won nine of her 21 chances.
There was just one point separating the pair at the end with Pera winning 129 points overall to Saville's 128. Â
Joining Pera in the next round is three-times grand slam champion Angelique Kerber, who beat Petra Martic 6-3 6-4.
German Kerber, who returned to the tour in January after 18 months on maternity leave, beat Martic behind some solid serving on a sunny centre court before rain delayed play in the evening.
"Follow your heart, enjoy what you love and dream big," Kerber said when asked what message she had for her daughter Liana.
Kerber will have her hands full when she faces in-form Latvian Jelena Ostapenko in the second round on Friday.
Meanwhile, 2021 winner Paula Badosa was forced to withdraw due to a lower back injury and will be replaced by Nadia Podoroska of Argentina.
"So sorry I have to withdraw from my favourite tournament," she wrote on social media.
"I tried everything to be able to play but wasn't enough. I'm having a very difficult time with my injury but I'm fighting every day to come back as soon as possible."
Italy's Camila Giorgi and American Katie Volynets were among the players to advance to the second round.
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