Sunday was Zaliukas' first domestic appearance of the season after he was forced to serve a four-match ban for picking up four red cards last term.
He insisted yesterday he had finally learned to control his temper, saying: "I now feel a calmer person. A lot of talking with the manager helped me. Now we understand each other, what we want from each other."
Laszlo handed Zaliukas the vice-captaincy at the start of the season, and he added: "Of course, I feel more important now. I need to show an example for the young boys - we have a lot of them - and the manager trusts me."
Dunfermline, seventh in the First Division, lost 4-1 to Hearts at the same stage of the competition almost exactly two years ago. The last time the teams met, the Fifers came out on top. That was in a pre-season friendly in July last year, when a Lee Wallace own goal separated the sides.