Michael O’Neill’s side were edged out by a single goal from West Ham talisman Marko Arnautovic.
The Austrian captain struck in the 71st minute after Peacock-Farrell had made two smart saves at the beginning of the second half to keep Northern Ireland level.
Stuart Dallas, who has only started two games for Leeds this campaign, looked sluggish in the opening stages, but soon settled into the contest.
The United midfielder forged Northern Ireland’s best opportunity when he flicked on for captain Steve Davis, who dragged his effort wide of the far post a few minutes into the second period.
Sheffield United’s Oliver Norwood, who qualifies for Northern Ireland through his grandfather, had created the away side’s best chance of the first half.
The 27-year-old delivered a delightful cross from deep towards Shane Ferguson, but the Millwall man was unable to direct his header on target.
Rotherham United striker Kyle Vassell, who was called up to the squad on Monday following Kyle Lafferty’s withdrawal, was handed his international debut when he replaced George Saville with 15 minutes remaining.
The risk of relegation is growing for Northern Ireland, who now need to win Monday’s match against Bosnia and Herzegovina in Sarajevo to keep their fate in their own hands.
Arnautovic, a constant thorn in the Northern Ireland defence, sprung the offside trap to get on to Peter Zulj’s pass before slotting the ball past Peacock-Farrell to settle a close contest.
Peacock-Farrell – involved in the mix-up that gifted Bosnia and Herzegovina a crucial second goal in Belfast last month – committed a major mental error in the first half when he picked up Jonny Evans’s back-pass to give away an indirect free-kick, and the Leeds goalkeeper was grateful to see Arnautovic fire into the wall.
While chances were few and far between in the first half the second half began with a flurry of opportunities.
First Austria could only half-clear Dallas’s long throw and Paddy McNair tried to curl the rebound home, but it was an easy enough save for Heinz Lindner.
The hosts then went straight to the other end where a mis-hit clearance fell kindly for Arnautovic, who bundled his way past Dallas before hitting a low shot that Peacock-Farrell diverted wide. The Leeds man then denied Sabitzer after his turn and shot, and Steven Davis missed the target after being played through on goal by Dallas.
Arnautovic would soon have his goal, providing the one real moment of class.
O’Neill went into all-out attack mode as Vassell went on for his debut, swiftly followed by Will Grigg, and the Wigan man was inches away from an equaliser when he twisted to head McNair’s 84th-minute corner on to a post. But that was as close as they would come as Austria held on for all three points.