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Jeff Hughes rattled the bar for the visitors just before the break, but that was the closest Keith Curle's side came to breaking the deadlock.
Brentford dominated for long spells and thought they had the three points in the bag late on, but Magpies defender Damion Stewart headed Sam Saunders' goal-bound free-kick off the line.
Bees striker Clayton Donaldson glanced a header inches wide when he got on the end of a Jake Bidwell cross headed back by Marcus Bean.
Donaldson also went close at the end of a flowing five-man move in a game where neither side looked like getting their noses in front.
The draw keeps County three points ahead of Brentford with the same games going into the last three games of the campaign.
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