All square at the break, following early goals by Stuart Armstrong and Jamie Hamill for the visitors, the hosts collected a comfortable three points thanks to Brian Graham, Gary Mackay-Steven and John Rankin who all found the back of the net to punish bottom-of-the-table Hearts.
Following a low-key start at Tannadice, the game sprung to life with a brace of goals during a six-minute period in the first half.
First, the hosts opened the scoring in the 16th minute when Armstrong latched on to Mackay-Steven's chipped assist to find the bottom left-hand corner of the net from the edge of the six-yard box.
But struggling Hearts were level thanks to Hamill who netted from the penalty spot following a foul by Mark Wilson on Jamie Walker.
And that was the way it remained until four minutes into the second half when United reclaimed the lead.
From Wilson's corner, Brian Graham rose to powerfully head home from close range and heap further misery on the Edinburgh club.
The Tangerines continued to dominate during the remainder of the contest but only sealed the win six minutes from time when Mackay-Steven collected Ryan Gauld's pass before curling the ball into the top left-hand corner of the net from the edge of the box to make it 3-1.
And with 91 minutes on the clock, John Rankin completed the scoring with a long range effort that clipped defender Danny Wilson on its way into the net.