The visitors opened the scoring on 15 minutes when a cross from right wing-back Philip Wallace was diverted into his own net by City central defender Dara Noonan, giving ‘keeper Sean Morgan no chance.
But after their poor start the home side began to assert themselves and were unlucky not to equalise before the break with fine efforts from Marty Havern and Philip Donnelly.
Immediately after the restart a long-range effort from Sean Mallon whizzed just wide of the Dergview upright with their stopper Jack Beggs beaten all ends up.
However, the visitors hit back immediately and Gareth Falconer missed a great chance to put his side further ahead when he blasted over the top from just eight yards out.
But Armagh were bossing the game at this stage and they deservedly equalised on 56 minutes when a 25-yard shot from Donnelly flew into the top left-hand corner of the net despite the best effort of Beggs.
In the final quarter City went quiet again and Dergview dominated but, despite this, Armagh had two of the best chances to claim all three points when late efforts from Stephen Murray and Dale Montgomery just went abegging.