The substitute gambled on a long ball forward and nodded over Fraser Forster (91+) to ensure the leaders' return to domestic duties after Champions League disappointment was a miserable one.
County had not lost since a 4-0 thumping at Celtic Park in December but though a repeat looked on the cards after 20 minutes, the ensuing turnaround instead stretched their unbeaten run to 11 games.
It had been a scrappy start on a treacly pitch before the breakthrough came in surprise circumstances, Charlie Mulgrew's corner from the right delivered with enough curl to evade Michael Fraser's flailing arm (15).
Neil Lennon's side doubled their lead just six minutes later when Gary Hooper chipped a Dylan McGeouch pass without breaking stride, a desperate Fraser palm again in vain.
Celtic old boy Rocco Quinn might have halved the deficit had the ball not caught awkwardly under his studs but Grant Munro breathed life into the contest soon after, controlling a half-cleared ball on his chest before lashing past Forster (30).
County were suddenly ascendant and when Iain Vigurs drove to the byline and found the back post, Sam Morrow bundled over his side's own quickfire second (36).
Anthony Stokes should have put Celtic back in front with the last kick of the half, drilling wide instead, while Hooper was unlucky to see his shot bounce off a home head and then the bar the other side of the interval.
Efe Ambrose had a bigger escape at the other end when his attempted header back to Forster gave Martin Scott a sniff and County's plan to defend deep and break in numbers looked increasingly astute.
Wohlfarth might have made his mark 10 minutes earlier but though he guided that Paul Lawson through-ball just wide, his predatory instinct paid off when Evangelos Ikonomou had launched a hopeful ball over the top.