Dungannon started brightly having the higher percentage of possession, but Ballinamallard looked dangerous on the break.
Harpur headed over after just five minutes while Teggart set up Ryan Mayse to volley on to the top of the netting.
With all the possession Swifts couldn’t find a chink in the home defence, with debut boy Jacob Britton impressing,and on 33 minutes Ciaran Martyn turned brilliantly on the edge of the penalty area to shoot just over Coleman’s crossbar.
Four minutes later former Ballinamallard players Lafferty and Mayse combined brilliantly to set up Mayse, but his effort was covered well by keeper Brush.
Then Armstrong and Curran combined well down the Ballinamallard right flank for Curran to pull a brilliant ball back to the 18 yard line, but the supporting Taheny’s effort was deflected and crashed just over the crossbar.
The second half saw a lively start by both teams.
Teggart went on a great run before delivering to Mayse, but his effort was brilliantly twarted by defender Smyth.
At the other end Curran good run on the right saw the ball pulled back to Taheny whose shot was was blocked.
Dungannon though had a high percentage of possession and Mayse set Lafferty up with a wonderful chip. The former Mallard striker took the ball on his chest and volleyed just over.
The all important score came on 80 minutes when a good run down the left flank saw the ball crossed to the back post and the unmarked central defender Arsmstrong was on hand to nod the ball in at the back post.
Good defending by the Swifts kept a clean sheet despite a brilliant opportunity at the near post for Curran.