The Championship Two leaders started strongly and immediately put the County Antrim visitors on the back-foot.
But United soon settled and forced City ‘keeper Sean Morgan into turning a fierce low shot around an upright.
Morgan was in action again on 10 minutes when he brilliantly saved a powerful Gerard Gillan header and, moments later, he could only watch as Hugh Og Boyle flicked another fine effort just wide.
A minute later, however, Armagh took the lead when Shea McGerrigan broke on the left and crossed into the box where Philip Donnelly tucked the ball home despite the best efforts of United stopper Brian Moore.
Armagh could have doubled their score moments later when Stepehn Murray and Donnelly almost rounded off a flowing move but the brave Moore came rushing out to smother the short-range shot.
In this free-flowing match Ballymoney’s Conor McKinley was unlucky to see his low shot diverted for a corner by Morgan while, at the other end of the park, Murray failed to finish off a clear-cut chance.
After the break the attacking pattern of play continued and Murray was again thwarted by the brillliant Brown who smothered his thunderous close-range effort.
On 53 minutes, however, Ballymoney deservedly got back on level terms when a pass from midfield into the Armagh box was latched onto by Conleth McCaughan and he dispatched the ball in style.
Both teams were now going flat-out for the winner and City had chances through McGerrigan and Cullen, while United’s Dairmuid Larkin had a golden opportuntiy to give his side the spoils.
Deep into injury-time a draw looked on the cards but then Armagh made one final effort to grab the winner.
The ball was floated into the Ballymoney danger area by McGerrigan and Murray headed goalwards. The ball, however, struck a United defender on thre arm and Dungannon whistler Lee Taverner immediately pointed to the penalty spot. Murray then stepped up and slammed the spot-kick into the net past the unfortunate Brown.
Sign Up To Our Newsletter
Sign up to our newsletter for major breaking news stories as they happen – right to your inbox.