With Levein's former club ahead by two points going into the last two SPL fixtures of the season, he knows victory at Tynecastle would hand United the impetus in the race for third place.
After finishing fifth last season, United's aim this term has been to grab the coveted 'best of the rest' accolade in behind the Old Firm.
A blip in form at the start of the year saw the Tangerines slip behind Hearts but in recent weeks they have begun to close the gap and Levein believes they have what it takes to finally overtake their rivals.
He said: "This weekend is going to be like a cup tie and I'm expecting it to be played like one.
"This is the biggest game of our season and all our work throughout the year has boiled down to this game.
"That's the way we want it because these are the kind of occasions you want to be involved in.
"If you'd told me at the start of the season we'd be going to Tynecastle with two games left having a chance to get into third place, I would've bitten your hand off.
"We asked the players a while back to get themselves into this situation and they've done it.
"At one stage, Hearts were five points behind but we've reeled them in a bit and know that getting third place is now in our own hands.
"That's all you want at this stage of the season because we know our fate is entirely down to what we do."
Levein will have captain Lee Wilkie available despite the defender's injury against Celtic on Tuesday evening.
The one-time Scotland international was hurt by a high challenge from Scott McDonald which sparked controversy in the aftermath of the game.
But although Wilkie, whose career has been blighted by serious knee problems, is feeling some effects of the midweek game, he is certain to play and Levein believes that is a major boost for his team.
He said: "Lee is a bit stiff and sore but I'm expecting him to be okay.
"He's the kind of lad who just gets on with things anyway and having him available is great news for us.
"Hearts have a big threat at set pieces so it's good to have him in the side and, of course, he's our captain and you always want to go into these sort of matches with your captain available."
The United boss also revealed Warren Feeney has probably played his final game for the club.
The striker, on loan from Cardiff, has been suffering from a pulled hamstring and has not been responding to treatment.
He has returned to England for a scan, is definitely out of this weekend's game and will most likely miss the season finale against Rangers.
The United boss revealed: "Warren Feeney is away to get a scan and I think that's him for the last two games.
"It's disappointing because he's done a good job for us but we'll get on with it.
"Fran Sandaza is back and I think playing 70 minutes against Celtic will do him the world of good.
"And another plus is that Scott Robertson is really coming along and I think he's fit enough to play half an hour or even 45 minutes."