Barry Smith's struggling side fell 18 points behind County who won thanks to Paul Lawson's 80th-minute strike which was followed by substitute Gary Glen's injury-time goal.
It now leaves them facing a huge task to avoid relegation while County continue to soar onwards and upwards in their first experience of the SPL.
This was a must-win game for the bottom team who already trailed their visitors by 15 points in their desperate battle to beat the drop. And they almost got off to a nightmare start inside the first minute of this clash with the Highlanders.
On-loan Celtic defender Lewis Toshney was short with an attempted back-pass to goalkeeper Rab Douglas. County midfielder Rocco Quinn was quick to latch on to the opening but just as he looked set make the hosts pay, Douglas raced off his line to clear the danger with a thumping clearance.
The visitors went into this game unbeaten in 2013 so were not lacking any confidence. That was shown in 13 minutes when midfielder Iain Vigurs left Dundee defender Gary Irvine for dead wide on the right.
Vigurs then cut inside and steadied himself before unleashing a left-foot shot which Douglas was relieved to see clear his near post. That was enough to sting the hosts into action and minutes later they mounted their fist real attack.
Brian Easton's clipped pass allowed Colin Nish to run clear into space down the left. The former Hibs and Kilmarnock man found himself in a decent position but his final ball into the box could not pick out any of his team-mates at the far post.
There was little incident in the second half until Lawson struck with a fierce strike which Douglas could not keep out and Glen made sure with a cool finish to round the Dundee keeper with the last kick of the game.