Gordon Chisholm's men could not score a crucial away goal in the driving wind and rain in Finland, but know that a 1-0 win at Tannadice in a fortnight will be enough to extend their European adventure.
MyPa started brightly with Derek Stillie forced to make a save from Tero Karhu in the opening seconds.
But United soon got to grips with the difficult conditions and controlled much of the first half.
Mark Kerr dragged a long-range effort wide of goal after nine minutes and less than a minute later Barry Robson was inches away after making a great run down the left flank.
On 12 minutes Robson had another go, this time from long-range, but under pressure from his marker he swiped his shot wide.
MyPa also had their chances, with Tuomo Kononen coming closest midway through the half as his 20-yard effort clipped the top of the bar.
But United effectively neutralised the threat of Brazilian striker Adriano Munoz who had no chances in the first half.
The visitors came under more pressure in the second half when MyPa won a stream of corners which kept Stillie on his toes.
Ten minutes into the half MyPa won a dangerous free-kick and Stillie was forced to tip Adriano's powerful effort over the crossbar.
But the visitors managed to withstand the pressure and Stillie kept a well-deserved clean sheet.
United had to wait until ten minutes from the end for their best chance which came from Jim McIntyre, who dived to meet a Mark Wilson cross and forced a good save from the keeper with his headed effort.