The goals came from Mxolisi Gumede in the first-half, Kennedy Mweene stretched Stars advantage in the second-half.
But the home side has only themselves to blame for finishing this match empty handed after spurning numerous goal scoring chances in the first-half.
The loss was the Team of Choices third consecutive league defeat and it keeps them rooted to the lower end of the League standings.
Gumede scored in the second minute when he powered a volley past Shu-Aib Walters in the United goals.
But, from then onwards United completely dominated proceedings for the remainder of the half with their relentless attacking play, keeping their supporters on the edge of their seats.
In the seventh minute, David Booysen had his powerful header well blocked by Stars keeper Kennedy Mweene.
Six minutes later, Kurt Lentjies should have leveled matters when he had only Mweene to beat, but he hit his attempt high over the crossbar.
There was more frustration for the home side a minute later, this time Musa Nyatama failed to get an attempt past the Free State shot stopper with the visiting defence nowhere to be seen.
Mweene was at full stretch in the 17th minute in keeping out Rudolph Bester’s blistering strike from range.
Lentjies had his second clear cut chance of the half in the 25th minute but once again he failed to hit the target from close range.
Five minutes later, United’s burly defender Mor Diouf found himself with shooting space in the Stars goalmouth but his effort lacked accuracy.
United continued harass the opposition defence during the remaining minutes of the half and the closet they came to finding the back of Mweene’s net was in the 43rd minute when Byrone Hendricks directed Lentjies corner kick onto the Stars upright.
The second-half was a dour affair as the home side failed to continue from where left off in the previous half.
Stars looked more solid in defence and were content with preserving their lead.
However, the only shot on target in this half came from a Stars player when Mpho Makola let rip with a shot from 20 metres away, requiring Walters to tip over.
Mweene put the final nail in United’s coffin when he fired home from the penalty spot with two minutes remaining.