The Premiership club are overwhelming favourites against Gary Caldwell’s side, who sit second bottom of the Championship. The teams drew 1-1 at Firhill last Monday night but Hearts are expected to progress this evening.
Manager Levein wants his players to show patience and control, with much of their focus centring around converting the kind of scoring chances passed up in Glasgow.
“I don’t think complacency will be a thing for us in this match. The carrot of having a semi-final spot available will be enough motivation for us,” Levein told the Evening News.
“Our chances of winning the match are increased by being back at Tynecastle. I understand what’s at stake and it’s up to me to get that message across.
“You can only want to win 100 per cent. We just need to do things properly, be patient, play with a calmness and take our opportunities. That’s the message, really.”
Midfielder Sean Clare, scorer of the winning goal in Saturday’s Premiership victory over Dundee, is expected to feature despite an ongoing hip complaint.
Striker Aidan Keena could be involved after pain relating to last year’s hernia surgery subsided.
“Sean has a little niggle with his hip but he has been managing it. Keena trained yesterday after having a few days off so we will see how he is,” said Levein.