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Northern Ireland shaded much of the game and largely snuffed out Wales' attacking threat, but they also lacked a cutting edge in attack.
Wales only managed one shot on target and the game was settled by the one moment of real quality at Parc des Princes.
Northern Ireland's resistance was finally broken when centre-back McAuley turned Gareth Bale's low, whipped cross into his own net.
It means Wales - in their first major tournament finals since the 1958 World Cup - will face Belgium or Hungary in the last eight in Lille on Friday.
Chris Coleman's side were blunted by their dogged opponents, but the scrappy nature of victory and the winning goal will matter little to their jubilant fans.
For Northern Ireland, the manner of defeat was galling, particularly for the 63-cap McAuley, who had scored in the 2-0 group win against Ukraine, which had helped his country reach the round of 16.
Both sides were playing a first match in the knockout stages of a major tournament since 1958, when they reached the World Cup quarter-finals.
Parc des Princes was awash with green and red as fans mingled and revelled in the enormity of the occasion - but the match failed to ignite during a cagey first half.
Northern Ireland's intention to frustrate their opponents was clear, depriving Wales of space with a careful pressing game held together by rigid positional discipline.
They also posed a counter-attacking threat, with one early break leading to a chance for Stuart Dallas, whose shot was saved by Wayne Hennessey.
Having beaten Russia so impressively in their final group game, Wales seemed neutered by Northern Ireland's containing strategy.
Coleman's men had struggled for goals during qualifying - scoring 11 in 10 matches - and this match demonstrated their occasional shortcomings against well-organised defences.
Bale saw one of his trademark dipping free-kicks saved by Michael McGovern but the Real Madrid forward's threat in open play was subdued.
That was until the 75th minute, when he unleashed a fizzing ball across the six-yard box and the sliding McAuley deflected the ball into the net.
This was the first match of the competition in which Bale failed to score, but his major contribution to Wales' winner was yet another example of the 26-year-old's ability to rise to the biggest occasions.
Tempers boiled over as Northern Ireland chased a late equaliser, with manager Michael O'Neill furiously animated on the touchline as he accused Wales of time-wasting.
Ashley Williams and Jonny Williams both received treatment on the pitch after colliding into each other, with the former holding his arm afterwards in a way which he suggested he may have broken or fractured part of it.
There was a heated exchange between O'Neill and Williams, with the Northern Ireland boss later claiming Wales coaches on the bench had told their captain to sit on the pitch to waste time.
The Swansea City centre-back stayed on the field until the final whistle but, with his arm in a sling afterwards, he could be a doubt for Wales' quarter-final on Friday.
Wales manager Chris Coleman on BBC One: "The good thing about these boys when we're not playing well is that they have spirit. And at times we were hanging on.
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"I'd rather be standing here in the quarter-final not playing at our best. We have to give credit to Northern Ireland - they made it very difficult to play against. They were the better team.
"We have to plan for the next game whoever it is. We'll enjoy this tonight."
Northern Ireland manager Michael O'Neill on BBC One: "It's devastating. We were the better team on the day.
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"I couldn't ask anything more of the players throughout the tournament.
"Gareth McAuley knows he has to make one of those decisions on the cross - he had to judge whether there was someone behind him or not."
Wales will wait to see who wins Sunday's last-16 tie between Hungary and Belgium before facing the victor in Lille on Friday. Northern Ireland head home after a memorable tournament, which included a victory over Ukraine in the group stage.
Match ends, Wales 1, Northern Ireland 0.
Second Half ends, Wales 1, Northern Ireland 0.
Corner,  Northern Ireland. Conceded by Hal Robson-Kanu.
Aaron Ramsey (Wales) is shown the yellow card.
Foul by Aaron Ramsey (Wales).
Steven Davis (Northern Ireland) wins a free kick on the right wing.
Neil Taylor (Wales) wins a free kick in the defensive half.
Foul by Josh Magennis (Northern Ireland).
Hal Robson-Kanu (Wales) wins a free kick in the attacking half.
Foul by Corry Evans (Northern Ireland).
Offside, Wales. Chris Gunter tries a through ball, but Aaron Ramsey is caught offside.
Gareth Bale (Wales) wins a free kick on the right wing.
Foul by Craig Cathcart (Northern Ireland).
Aaron Ramsey (Wales) wins a free kick in the defensive half.
Foul by Kyle Lafferty (Northern Ireland).
Delay over. They are ready to continue.
Substitution, Northern Ireland. Josh Magennis replaces Gareth McAuley.
Delay in match Jonathan Williams (Wales) because of an injury.
Chris Gunter (Wales) wins a free kick in the defensive half.
Foul by Jonny Evans (Northern Ireland).
Foul by Neil Taylor (Wales).
Kyle Lafferty (Northern Ireland) wins a free kick on the right wing.
Substitution, Northern Ireland. Niall McGinn replaces Oliver Norwood.
Own Goal by Gareth McAuley, Northern Ireland.  Wales 1, Northern Ireland 0.
Attempt blocked. Aaron Ramsey (Wales) right footed shot from outside the box is blocked.
Substitution, Northern Ireland. Conor Washington replaces Jamie Ward.
Steven Davis (Northern Ireland) is shown the yellow card for a bad foul.
Gareth Bale (Wales) wins a free kick on the left wing.
Foul by Steven Davis (Northern Ireland).
Substitution, Wales. Jonathan Williams replaces Joe Ledley.
Attempt blocked. Aaron Ramsey (Wales) right footed shot from outside the box is blocked.
Corner,  Northern Ireland. Conceded by Chris Gunter.
Corner,  Northern Ireland. Conceded by Ben Davies.
Neil Taylor (Wales) is shown the yellow card for a bad foul.
Foul by Neil Taylor (Wales).
Jamie Ward (Northern Ireland) wins a free kick in the attacking half.
Attempt saved. Gareth Bale (Wales) left footed shot from outside the box is saved in the bottom right corner.
Gareth Bale (Wales) wins a free kick in the attacking half.
Foul by Oliver Norwood (Northern Ireland).
Attempt saved. Oliver Norwood (Northern Ireland) right footed shot from outside the box is saved in the bottom left corner. Assisted by Stuart Dallas.
A:
Wales reached the quarter-finals of Euro 2016 as Gareth McAuley's own goal gave them victory over Northern Ireland in a tense last-16 encounter.