The highly regarded Peake could have been out first ball, but instead played an early career-shaping knock to steer Victoria to the tricky chase of 231 at Adelaide Oval on Tuesday.
After barely surviving a hat-trick ball to begin his stay, the 19-year-old showed composure beyond his years to finish unbeaten on 70 from 147 balls.
Seamer Fergus O'Neill (33*) provided great support for Peake in an unbeaten 84-run partnership for the Vics, who lost Sam Harper (29) at an important time when the wicketkeeper was batting well.
O'Neill hit the winning runs in the dying stages of day four, upsetting SA in their first match since breaking their 29-year Shield drought in March.
It was only Peake's second Shield game for Victoria, and fifth first-class match, after playing three matches for Australia A this year.
Peake's clutch performance would have delighted Australian selectors, who have been tracking the young gun's progress closely.
It came after SA quick Jordan Buckingham (3-43) fell agonisingly short of a hat-trick, with Henry Hunt dropping a sharp chance at short leg.
After dismissing former Test players Marcus Harris (13) and Peter Handscomb (0) in consecutive balls, Buckingham had the opportunity to make history.
Peake clipped the hat-trick ball off his legs, but Hunt put down the reflex chance to deny Buckingham and change the momentum of the chase.
In the first innings, Handscomb posted an outstanding innings in a reminder he might not be done at international level.
Handscomb, whose most recent Test was against India in March 2023, faced 180 balls and hit seven fours and two sixes.
Half of his 18 Shield tons have been against SA.
Opener Henry Hunt and Jake Lehmann starred with centuries in SA's first innings.
But SA captain and Test hopeful Nathan McSweeney endured a horror Shield opener, out for a duck and 6.
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