United started the game in the best possible fashion as they went ahead after 30 seconds when Chris Erskine collected a cross and volleyed at goal, and his strike hit off Stuart Armstrong to find the net.
The visitors got back into the game in spectacular fashion as they won a free kick 25 yards from goal after Calum Butcher committed a foul. Greg Stewart fired his strike over the wall and into the top corner, leaving Radoslaw Cierzniak no chance.
Jackie McNamara's side took full control of the game when John Rankin lifted a cross into the box, which found Erskine unmarked in the middle and he made no mistake slotting his strike past Schenk.
United made it four just before the break when Mackay-Steven latched on to a through-ball to beat the offside trap, and the striker kept his composure to find the bottom corner with a low effort.
In the second half, Paul Hartley's men tried to rally to get back into the game and went close as James McPake's effort was parried by Cierzniak, but Paul McGowan and David Clarkson failed to turn the loose ball into the net.
Cierzniak reached out at full stretch to tip a headed effort from Jim McAlister past the post after the midfielder had latched onto a cross into the penalty area to keep his side's lead comfortable.
United netted their fifth goal of the afternoon when Jaroslaw Fojut rose highest in the penalty area from a corner from the right to power a header past Schenk.
Chris Telfer compounded the misery for the visitors when he added a sixth goal as he collected a pass from Mackay-Steven to drill an effort into the net. Luka Tankulic did add a late consolation for Hartley's side, but the day belonged to United.