A goalkeeping blunder by County's Bartosz Bialkowski gifted the Bees a first-half lead when Toumani Diagouraga's tame side-foot shot slipped through his grasp and rolled into the net.
The Pole was substituted at half-time but there was little his replacement Kevin Pilkington could do to stop the hosts from making it 2-0 after 70 minutes.
Bradley Wright-Phillips latched onto a throughball from Tom Adeyemi to smash a rasping shot inside the far post for his first goal for the Londoners.
But Brentford were pegged back four minutes later when Jake Bidwell sent Alan Judge tumbling inside the box and the Magpies midfielder reacted quickest to tap home the rebound when Jamal Campbell-Ryce's penalty was saved by Simon Moore.
Uwe Rosler's team, who dominated the first half and saw Wright-Phillips fire against the upright, had to hold on in the dying stages.
Judge saw a bobbling long-range effort saved at the second attempt by Moore and substitute Enoch Showunmi twice saw shots cleared as the Bees dropped deeper and deeper.
Brentford's top scorer Clayton Donaldson could have settled their nerves on the hour mark but fired straight at Pilkington, while Moore had to be brave to deny the onrushing Showunmi deep into injury time.