A Rudi Skacel double and goals from Darren Barr, Danny Grainger - from the spot - and Ryan McGowan had Hearts on easy street. Hibernian's consolation goal came before the break from skipper James McPake.
The one-sided game saw Hibernian defender Pa Kujabi sent off just after the break for picking up his second yellow card for a foul on Suso Santana in conceding the penalty which Grainger tucked away.
"It is not a moment to be speaking about my future," said the former Sporting Lisbon boss.
"I don't know if it my last game, I will see. It is not winning the cup or not winning the cup that can make me stay or not, there are a lot of things to talk about.
"The important thing is Hearts. It is probably my biggest achievement as manager."