Goalkeeper Livakovic saved spot-kicks from Takumi Minamino, Kaoru Mitoma and Maya Yoshida to send Croatia through to the quarter-finals.
Danijel Subasic had likewise kept out three penalties in a last-16 shoot-out during a run to the final in Russia four years ago, with Croatia now having won each of its three World Cup knockout ties that have gone all the way.
The result was a little harsh on Japan, which had led through Daizen Maeda before Ivan Perisic equalised, although neither side impressed ahead of a meeting with either Brazil or Korea Republic in the next round.
An entertaining start was not an indicator of what was to come. Shogo Taniguchi headed wide at one end and Perisic was denied at the other, but there was not another clear-cut chance until the opener two minutes before half-time.
Ritsu Doan's cross after a short corner reached the centre of the area, where Maya Yoshida's attempt at a shot succeeded instead in teeing up Maeda for a close-range finish.
Croatia had not looked like crafting a goal of its own, but it was level 10 minutes after the restart when Perisic met Dejan Lovren's delivery with a superb header into the bottom-right corner.
Although Ante Budimir soon nodded off target, opportunities remained scarce and Lovro Majer dragged wide with the final kick of extra time to condemn the tie to penalties.
Livakovic kept out Japan's first two attempts, with his save from Mitoma particularly impressive, and Croatia could ease through even with Marko Livaja clipping a dreadful effort against the post.