Cathal Beacom's late free-kick gave Ballinamallard United three important points as they strive to get away from relegation danger.
Beacom scored direct from the 81st-minute set-piece to keep the Mallards four points clear of one-from-bottom Warrenpoint who beat Institute.
"It just took one player to step up and produce that bit of magic," said United manager Whitey Anderson.
"It is a massive difference getting three points instead of one."
Dungannon boss Darren Murphy said: "There was a lot to play for.
"Both defences did well and it took that bit of brilliance from young Beacom.
"Apart from that there were few chances in the game."