City, without a competitive match for three weeks, struggled to find an early opening despite dictating play for long periods.
But, on 13 minutes, they did take a deserved lead when a long kick-out from goalkeeper Sean Morgan eluded the United back-four and Armagh midifielder Philip Donnelly nipped in to place the ball over onrushing stopper Mark Winstone.
In a scrappy first-half Winstone again came to his team’s rescue when he saved low to his left after superb approach play from City’s wing-back Dale Montgomery and captain Liam Cullen.
After the break Armagh began to show better form and strung several dangerous attacks together.
But Winstone was at his best to deny Donnelly, striker Stephen Murray and midfielder Andy Moore as the home side tried desperately to wrap up the match with a second score.
And, in the final minute, the insurance goal finally arrived when the prolific Murray drilled a low 20-yard shot past the outstretched Winstone – to record his 80th goal in 98 appearances for the Holm Park club.
Not City’s best showing this season but they will just be happy to be in the Irish Cup fifth round hat for this Wednesday’s draw.