Donegal Celtic have opened up a five-point gap on basement side Distillery after winning the relegation showdown.
Distillery's best chance came on nine minutes with William Garrett heading over from close range.
White keeper Lee Windrum tipped over Stephen O'Neill's powerful header as DC began to control the game.
O'Neill scored the crucial goal on 54 minutes, firing home after the hosts failed to clear a corner to clinch DC's first away win of the season.
With just four games left Distillery face an uphill battle to avoid finishing in the automatic relegation spot.
Andy Hunter's long throw set up Garrett for the early Whites opening while Mark Miskimmin was the provider for O'Neill's first-half header.
It was a game of few chances although the west Belfast visitors looked more likely to score and O'Neill thundered home the only goal early in the second half.
"We totally dominated the first half and it was a win we thoroughly deserved," said Donegal Celtic boss Pat McAllister.
"I told the boys to be patient and the chance would come, and it did with Stephen O'Neill.
"The players have been superb for the last few weeks and have shown tremendous character.
"There is still a long way to go but we feel we can compete with anyone at the moment."