Goals from Tope Obadeyi and Mark Connolly sealed a well-deserved three points for the hosts who were the better side for large periods of the game.
Both goals came during a three-minute spell just after the hour mark, to set Killie on their way to a fourth home win in five games this season.
With 63 minutes on the clock, Josh Magennis laid the ball out wide to Eremenko whose precise low pass was collected by Obadeyi who held off a couple of defenders before locating the far corner of the net.
And shortly afterwards, Killie took an even firmer grip on proceedings when Eremenko’s corner was powerfully headed home by Connolly.
As United tried to reduce the deficit, Gary Mackay-Steven blasted over while Chris Erskine’s low shot was saved by substitute keeper Conor Brennan.
Kilmarnock came mighty close to extending their lead four minutes from time when only a brilliant save by Radoslaw Cierzniak prevented Robbie Muirhead from finding the top corner with a fierce strike from outside the box.
Kilmarnock had also dominated a goalless first half and should certainly have been ahead by the break.
Magennis came close to opening the scoring in the seventh minute when his powerful header from Chris Chantler’s cross was superbly pushed clear by a diving Cierzniak.
Three minutes later the hosts were presented with another excellent chance when Obadeyi blasted over from 10 yards.
And as Killie continued to control the early stages, Eremenko smashed a long range free-kick wide of the right post.
United’s first real effort came on 26 when Sean Dillon’s looping cross was headed wide by Nadir Ciftci.
However, Magennis was just inches away from giving Kilmarnock the lead on 38. Following a quick punt upfield by Eremenko, Magennis lobbed the ball over the advancing Cierzniak only to see it land six yards short and then bounce off the plastic playing surface before clipping the top of the crossbar.
Yet Kilmarnock were not to be denied after the break, as they ended a run of five straight defeats at the hands of United to move third in the table.