Dundee United saw off the challenge of a spirited Rangers side to set up a scenario whereby Celtic could win the Scottish Premier League title at Ibrox.
Keith Watson's stunning 20-yard strike fired the home side ahead before Jon Daly doubled the lead from close-range.
John Rankin's own goal gave Rangers hope after Sone Aluko's shot from inside the penalty area was deflected in.
But they could not level and Celtic could triumph on their rivals' turf.
That situation would unfold if Motherwell fail to win at Kilmarnock the day before next Sunday's Old Firm encounter.
Ally McCoist's side were by far the most threatening in a stilted start and Steven Davis fed Salim Kerkar after Sean Dillon dallied on the ball.
However, the French-Algerian saw any opportunity snuffed out as Dusan Pernis rushed to clear from the edge of his box.
United were failing to find first gear and were almost made to pay for their lethargy.
Kerkar slalomed past the challenge of a handful of United defenders before knocking it past Gavin Gunning. However, he could not direct his left-foot effort from close range on target.
Peter Houston's men then stunned their opponents as they took the lead with a bolt from the blue after 37 minutes.
Rangers failed to deal with Paul Dixon's long throw-in into the penalty area and the ball sat up perfectly for Watson to drill past McGregor into the top right-hand corner of the net from 20 yards.
United started the second half brightly and doubled their advantage two minutes after the break.
Dixon pressured Andrew Mitchell, allowing Mackay-Steven to gain possession and send a sumptuous cross over from the left between two defenders for Jon Daly to finish first time.
Sone Aluko replaced debutant Mitchell a couple of minutes later after the youngster's error as Rangers manager McCoist searched for a route back into the game.
The Nigerian was the catalyst Rangers needed and on 59 minutes he conjured up some sublime skill with a stepover and a nutmeg to advance into the penalty area.
His shot was deflected by the sliding challenge of John Rankin and looped up over Pernis to reduce the deficit.
Rangers rallied and Bedoya's left-footed drive was easily saved by the Tannadice keeper before Lee McCulloch, at the other end, bravely headed Johnny Russell's goal-bound drive over the bar.
However, they could not find a way through again and now face the prospect of their age-old rivals toasting the league championship on their home turf.