On a cold North-East afternoon there was little to cheer in the opening 45 minutes, although White did come to his side's rescue at the opposite end when clearing an Alun Armstrong effort off the goal-line in the 33rd minute.
Prior to that, play had been scrappy and it was easy to see how both of these sides had lost their previous three games. For Darlington manager Dave Penney his honeymoon period is very much over after an unbeaten six-game start to his reign.
The second half began brightly, however, and in the 49th minute Darlington winger Neil Wainwright fired narrowly over the crossbar from the edge of the area.
Six minutes later the home side thought that they had got themselves a penalty when Barry Conlon's shot appeared to strike the arm of Ian Ross. But the referee waved play-on, much to the disgust of the home side, who had also seen the official rule out a goal from Darren Holloway in the 33rd minute.
So as Darlington lost their composure the visitors grew in confidence and they ended the game in a strong fashion.
In the 70th minute the impressive Andy Parkinson fired against an upright after wriggling his way to the bye-line. And then, five minutes later, defender Gary Silk tried his luck with a shot from the edge of the area that Darlington keeper David Stockdale claimed after two attempts.
County striker Lawrie Dudfield had two quick-fire opportunities to break the deadlock. In the 76th minute he fired across the face of goal and, in the visitors' next attack, he raced clear inside the area before firing straight at Stockdale.
The clincher came six minutes from time when a right-wing cross from Jay Smith found White inside the area and he rose highest to power the ball into the net from ten yards out.