Levein's United take on the same opponents again in the SPL on Sunday and, with the fixture list throwing up a quirk of fate, he is hoping for the same outcome.
During his three years, Levein has transformed United from perennial relegation battlers to a side with genuine aspirations of challenging the Old Firm.
But while they have significantly closed the gap on Rangers and Celtic over the past three seasons, Levein knows Walter Smith's beleaguered side remain dangerous opponents.
He said: "It's a coincidence that we're playing Rangers three years on and if it's the same result, I'd be delighted.
"It has been some three years for both clubs. Obviously, we've overhauled things here but Rangers have also gone through a lot of changes.
"Paul Le Guen was the manager in that first game but, since then, they've appointed Walter and he gave them a massive lift.
"They've not had their troubles to seek in recent weeks but, for me, that makes them dangerous.
"They are a wounded animal at the moment and we all know that when a club like Rangers gets criticised, they come out fighting.
"With Walter in charge, they have a man with loads of experience who can lead them through this."
Rangers were tipped towards crisis following their humiliation at the hands of Romanian minnows Unirea Urziceni in the Champions League two weeks ago.
News of their deepening financial problems have exacerbated the hurt at Ibrox but Levein insists they are a better side than the critics suggest.
He said: "Since the European game the other week, they've had a decent result against Hibs and got into the cup semi-final.
"It's easy to forget that they're still unbeaten in the league, although the amount of draws has cost them points.
"We only have to look to the final game of last season, when they beat us 3-0 to win the title, to see how dangerous they can be."
United were dumped out of the Co-operative Insurance Cup at St Johnstone on Tuesday and Levein said: "I'm looking for a positive reaction from the players.
"We were really disappointed with our performance and have talked about it.
"But how we bounce back is the main thing now. This is a massive game, it's against the champions and on the telly, so there are huge incentives."
United have a doubt over goalkeeper Nicky Weaver, who has a thigh strain, so player-coach Steve Banks is waiting in the wings.
Levein revealed: "Nicky joined in training on Friday but hasn't kicked a ball yet.
"He's got a thigh strain so it's a bit of a dilemma for us.
"I don't want to end up playing him with someone else taking the goal-kicks for him.
"Because if you go down that road, what do you do in open play?
"So it's a case of waiting to see, I'll give him every chance to make it.
"But if he doesn't then we've got Steve Banks, who is a top quality keeper and has loads of experience."
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