This was a must-win game for the bottom team but they almost got off to another nightmare start inside the first minute.
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 unleashed a left-foot shot which Douglas was relieved to see clear his near post.
The visitors remained slightly on top and midway through the first half they threatened the Dundee goal again. Alex Cooper drove forward and rifled in a low 25-yard drive which flashed narrowly past Douglas' left-hand post.
On 36 minutes Dundee were claiming a penalty when Jim McAlister's shot appeared to strike Scott Boyd's hand at point-blank range, but referee John McCendrick was close by and waved play on.
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.