The goalkeeper made a hat-trick of spot-kick saves after their round-of-16 tie went to penalties following a 1-1 draw after 120 minutes of nail-biting football.
The early exchanges defied the expectations of a tight 90 minutes, as Japan came close to scoring with their first attack when Shogo Taniguchi headed wide.
Ivan Perišić should then have put his side ahead at the other end as he burst through on goal after brushing past Takehiro Tomiyasu, only to criminally shoot too close to Shuichi Gonda when one-on-one.
Japan responded quickly, with Waturu Endo having a long-range effort tipped over the bar, but Zlatko Dalić’s side were in the ascendancy now, with Luka Modrić forcing Gonda into a superb diving stop, while Ante Budimir nodded wide.
Kaoru Mitoma had the best chance, carrying the ball 50 yards before having a powerful drive pushed over the bar, while Lovro Majer dragged a low effort wide in injury time, meaning penalties were needed to find a winner.
Maya Yoshida had a third effort stopped by Livaković before Mario Pašalić netted the winning penalty, ensuring Croatia go through to face either South Korea or Brazil, while Japan suffered a fourth round-of-16 defeat.