The German beat Kelvin Wilson and Fraser Forster to a long ball to head into the net as the hosts stunned Celtic and consolidated their status as the Clydesdale Bank Premier League's form team of 2013.
The win looked highly unlikely after 21 minutes after Charlie Mulgrew had scored direct from a corner and Gary Hooper chipped home as goalkeeper Michael Fraser endured a nightmare six minutes.
But County also scored twice in six minutes. A stunning volley from Grant Munro and Sam Morrow's close-range finish got them level before the break.
And they emulated their 2010 Scottish Cup win over the Hoops when German substitute Wohlfarth netted his first County goal.
County have not lost since a 4-0 defeat at Celtic Park on December 22, taking 27 points from their subsequent 11 matches - two more than Celtic have claimed in 12 games.
Efe Ambrose and Rami Gershon came into a three-man Celtic defence as Neil Lennon made five changes following the Champions League defeat by Juventus.
Dylan McGeouch, Miku and Anthony Stokes also came in after Victor Wanyama, Adam Matthews, Georgios Samaras and Emilio Izaguirre picked up injuries in Turin, while Kris Commons dropped to the bench.
County were without the in-form Ivan Sproule and suspended captain Richard Brittain while Fraser continued to deputise for the injured Mark Brown.
Conditions were far from ideal with a sandy, bumpy pitch and an icy, strong wind above but the visitors adapted well initially. Ambrose's long ball reached Hooper thanks to some hesitant defending but Fraser stood up to push the striker's shot wide.
The resulting corner was cleared but Mulgrew got another chance to deliver and he made the most of it as he swerved the ball past Fraser into the top corner.
Fraser saved well from Miku after the Venezuelan had played a one-two with Hooper but he was soon beaten again by a soft goal.
McGeouch laid the ball back for Hooper 18 yards and the Englishman chipped the ball towards the far post with Fraser again only able to help it into the net as he was caught off his line.
The Celtic fans had been singing incessantly from before the first whistle and their afternoon looked like being one long party, but County had other ideas.
Rocco Quinn made two good runs forward and got a shot away at the second attempt, but the angle gave Fraser Forster a comfortable save.
The comeback started in the 30th minute with a spectacular first-time effort from Munro.
Celtic initially cleared an Iain Vigurs free-kick but Mihael Kovacevic returned a high ball into box. Kelvin Wilson won the aerial challenge but his header fell for Munro and the big defender unleashed a stunning left-footed strike into the top corner past a helpless Forster.
County were level six minutes later. Vigurs nutmegged Mulgrew on the right wing and skipped round Joe Ledley before hanging a cross to the far post which held up in the wind. Morrow and McGeouch challenged for the ball and the County forward reacted quickest to force the ball home from close range.
Stokes should have put Celtic back in front with the last kick of the half but he drilled wide from 15 yards after Miku had found him unmarked.
Vigurs curled a free-kick not far wide before the second half settled into an early rhythm of County defending but breaking dangerously.
The hosts had a let-off after Beram Kayal played Hooper through. Fraser palmed out the striker's shot and it bounced off the head of Kovacevic and off the top of the bar.
But Ambrose had a bigger escape after making a mess of his header back to Forster following Quinn's deep cross. The Nigerian set up Martin Scott but the County midfielder snatched at his chance and hit it straight at Forster.
Celtic were finding it difficult to break County down and their fans were much quieter as Kovacevic, Stuart Kettlewell and Munro all hit ambitious efforts wide as County gained the ascendancy.
Wohlfarth had a great chance with 10 minutes left when Paul Lawson played the ball through. The German got there before Forster but guided the ball just wide.
Hooper turned and shot just past but that was a rare foray forward for Celtic and the hosts snatched a famous win when Wohlfarth reached a long ball by Evangelos Ikonomou to head past the onrushing Forster.
- Sports & Recreation
- Fraser Forster
- Michael Fraser
- Gary Hooper