Derek Adams, the County manager, was on the scoresheet with an extra-time double the last time the Highlanders defeated the Tannadice side, in a Scottish League Cup tie in 1998.
The defiance that has characterised the Dingwall team's spirited impressive first season in the top flight fired them on again as they produced an accomplished and controlled display.
United, who had Barry Douglas sent off after 65 minutes, turned in a spirited performance in pouring rain but rarely looked like scoring and a costly defeat all but rules them out of the running for Europe.
Jackie McNamara admitted such after the match, but revealed the club would be appealing Douglas' red card.
"I think that it is over for Europe, realistically," said McNamara. "It would be very difficult for us. I thought it was a game we had to win, and I'm very disappointed."
County lined up as they had in the 2-2 draw at St Johnstone last Sunday. Scott Boyd, available again after suspension, was on the bench while Andre Hainault, the Canadian internationalist, kept his place in the defence.
McNamara, still without Johnny Russell, kept the same starting XI from last Friday's defeat by Motherwell.
A poor Dingwall surface, still suffering badly from mid-season flood repairs, made for erratic touches and helped neither side. United managed a degree of fluency on the break without seriously threatening Michael Fraser's goal often enough in the first half.
County looked the more dangerous in the final third as a raggedly competitive first half unfolded. Iain Vigurs was in the thick of action again for County but squandered a fifth-minute chance when he was given a clear sight of goal after early urgency from the hosts.
Radoslaw Cierzniak, the United goalkeeper, was alert and sharp off his line as Sproule burst clear on to a Paul Lawson pass five minutes later. Willo Flood's craft was evident in prompting United's attempts at retaliation, with the Thurso-born Gary Mackay-Steven, back to face the club where he played as a youth, a willing recipient.
Not much was clicking for United, but Mackay-Steven's promising foray after 15 minutes won a corner.
Stuart Armstrong's delivery served up a decent chance for Jon Daly but the Irishman's close-range header failed to trouble Fraser.
Minutes later, Sproule passed to Steffen Wohlfarth, County's imposing German frontman and he showed good strength and control before being shut down by the United defence.
Wohlfarth's threat was underlined again four minutes later and John Souttar was perhaps lucky to escape with a yellow card after he cynically handled the ball to prevent the former Bayern Munich reserve player breaking clear.
United, though, could claim the closest call in front of goal on the half-hour mark. Douglas's left-footed free-kick was measured perfectly for Daly and this time he connected sweetly, only for Fraser to leap acrobatically to touch it to safety. The rest of the first half fizzled out and, as the second opened, the match was crying out for an injection of ideas. County's Richard Brittain shot right over the away stand with one attempt. However, there was no lack of composure in evidence as the home side swept into a 54th-minute lead.
Lawson's diagonal ball found Vigurs, who controlled it on the left of the penalty box, dragged the ball into space and delivered with a deft flick, which found Sproule waiting at the far post to head home for his sixth goal since joining the club in January.
United's chances of recovery suffered a setback when Douglas was shown a straight red card for crashing recklessly into Sproule.
County pressed on and Wohlfarth set up Sproule for a chance he failed to grasp. Lawson curled the resultant loose ball over the bar.
The home momentum was building and Vigurs shot just wide from a Sproule cross. A second goal was inches away after 77 minutes when Vigurs swept a pass across the United box. Brittain connected sweetly but his right-footed shot cracked the top of the bar. The captain also fired over another opportunity created by Vigurs.
Inevitably, there were some nervous moments for the hosts late on as United went in search of an equaliser in the three minutes of added time, but the hosts held on.
Adams said: "We controlled the game. It was a very good performance and nice to get a home win.
"We've got three difficult games now, Motherwell, Celtic and Inverness. The derby finishes the season and it could be pivotal."