Wales had hogged possession and spent most of the second half on the front foot but were unable to break down a resilient Irish rearguard until Bale produced the only moment of genuine class in the match after 75 minutes.
The Welsh talisman, who had been expertly shackled for the entire encounter, was allowed a few metres of space and took the opportunity with relish, whipping a devilish cross into the box that McAuley could only turn into his own net.
It was a cruel blow for the Irish, who had more than held their own in a scruffy encounter but lacked the quality to craft enough chances to trouble a Wales side who will now face Hungary or Belgium in the last eight in Lille on Friday.
"They were better than us today really," said Wales coach Chris Coleman, whose side reached the last eight of a major tournament for the first time since the 1958 World Cup.
"They played very well. We showed a lot of heart, a lot of courage. We showed another side to our game. We hung on and we came through. It is a fantastic achievement."
For Nortehrn Ireland coach Michael O'Neill it was a bitter pill to swallow.
"The lads have been tremendous," he said. "They have shown pride in playing for their country but when it ends like it did today, it is very cruel. I don't think we got what we deserved...
"I think at international football when you are a small nation you have to be strong tactically and make yourself hard to beat and we have certainly done that."
Saturday's encounter, the first between two of Britain's Home Nations in the knockout stage of a major tournament, was pitched as a battle between a Wales side dotted with individual talents and the resolute collective spirit of Northern Ireland.
Having not beaten Wales in eight attempts in a run stretching back to 1980, it was clear from the opening moments that the Irish were not going to let their opponents, and Bale in particular, impose themselves on the clash.
WOEFUL HALF
O'Neill's side snapped into tackles and stuck rigidly to the script of getting men massed behind the ball, while looking to capitalise on Welsh frustration by occasionally venturing forward.
The craft and guile that Wales needed to break them down was lacking in a woeful first half, where the nearest Coleman's side came to breaking the deadlock was an Aaron Ramsey effort that was rightly ruled out for offside after 18 minutes.
Northern Ireland had less of the ball but looked marginally more threatening with Stuart Dallas drawing the first save of the match out of Wayne Hennessey from just inside the box and Jamie Ward forcing the Wales keeper to tip his shot over.
The lack of quality ensured the Parc des Princes atmosphere became progressively more muted as the first half wore on before the tie flickered back into life at the start of the second.
Wales forward Sam Vokes headed wide from 10 metres and the tournament's joint-top scorer Bale, who had already netted from two free kicks in the group stage, forced Michael McGovern into a sprawling save with a swerving strike from a set piece.
The goal the game craved finally arrived 15 minutes from time as a result of the only real moment of class in the match.
Bale dashed down the left and fizzed an irresistible cross into the six-yard box that McAuley could only divert into his own net as he stretched to clear, with Wales substitute Hal Robson-Kanu waiting behind him ready to turn the ball home.
Northern Ireland could muster little in reply and resorted to lumping long balls into the Wales box in the final stages, before the final whistle sparked raucous celebrations among the red-clad fans packed into the stadium.
(Reporting by Toby Davis; editing by Editing by Ken Ferris)
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