The trip to Nicosia was seen as an ideal chance for manager Michael O'Neill to register a first away win as boss.
But his side were forced to hang on when West Brom defender McAuley was harshly dismissed in the 75th minute for a late tackle on Dimitris Christofi.
Northern Ireland have now won just once in their last 20 outings.
Things may have been different had Martin Paterson's 12th-minute header not been brilliantly saved, but there was little excuse for the lack of another clear-cut chance in the remaining 68 minutes.
The fixture had clearly failed to grab the attention of the Nicosia public, with the lure of free entry not enough to tempt more than a scattering of home fans, who were comfortably out-sung by a hardy away contingent.
It briefly seemed as though the contest on the pitch would follow a similar pattern as Northern Ireland dominated the ball in the opening exchanges.
Jamie Ward took an early run at Charis Kyrakou and, when his cross was cleared, Chris Brunt's volleyed effort was bravely blocked.
Paterson must have thought he had opened the scoring in the 12th minute when he rose at the near post to meet Niall McGinn's right-wing cross.
The Huddersfield striker did everything right but, unfortunately for him, so did the alert goalkeeper Antonis Giorgallidis, who clawed the ball back to safety.
That was as good as it got for O'Neill's men in the opening period.
There were loose passes all across the park, Steven Davis, Oliver Norwood and Alex Bruce all guilty in that regard, while Brunt looked lost positionally.
The live-wire Dimitris Christofi was at the heart of an improved Cyprus performance, pushing and prompting from the right flank and cutting inside when space allowed.
The winger might have gone down in the area under the attention of Bruce but admirably stayed upright.
Northern Ireland lost their shape as the half progressed and were penned in at times as Christofi, Efstathios Aloneftis and Nestor Mytidis combined to fashion a series of half-chances.
Several did not get as far as testing Alan Mannus, but there were tangible nerves in the Northern Ireland back line and McGivern was successfully double-teamed by Christofi and Charis Kyriakou on more than one occasion.
Northern Ireland were ragged by the 38th minute, when Cyprus almost prised them open with a fine move.
A patient build-up fed the ball to Aloneftis, who feigned to shoot before chipping towards the advancing Christofi.
His shot may have been creeping over, but Mannus was in no mood to find out and palmed it over the bar.
By the time the whistle went, the visitors were content to survive unscathed.
O'Neill made two changes during the interval, though he would have been forgiven had he made more drastic surgery.
Roy Carroll and Kyle Lafferty were summoned in placed of Mannus and Paterson, with Lafferty ending a six-month absence from the national side.
A promising break opened up in the 50th minute, Brunt making big inroads down the left and offloading to Ward, who got the ball trapped under his feet before he could bring Lafferty into play.
The Derby forward went closer seven minutes later, feeding off McGinn's reverse pass but dragging his shot a yard wide across goal.
O'Neill went to his bench in pursuit of the win, sending on Billy McKay, Paddy McCourt and Shane Ferguson.
But, with 75 minutes gone, it became a salvage job when McAuley was shown a harsh red card.
His challenge on Christofi was clumsy but there was hardly a scoring opportunity on the cards.
McKay was duly replaced by Rory McArdle, having been on the field just 16 minutes, and the stalemate was ensured when Carroll got down well in the last minute to smother Andreas Makris' close-range effort.