Poole fired the Londoners ahead after 36 minutes with a fine left-foot shot after Charlie MacDonald had pulled the ball back into his path from the by-line.
But when County levelled after 65 minutes, Poole was again involved. He handled a cross from Adam Tamm and Jamie Forrester kept his cool to send Ben Hamer the wrong way from the spot.
Both sides are unbeaten since the opening day of the season and performed in a manner which showed why.
Three times in the space of five first-half minutes County went close as Myles Weston angled a shot just wide and Hamer made spectacular saves from Matt Hamshaw and Delroy Facey.
But Brentford scored against the run of play and forced County to work hard to rescue a point. Jamie Clapham thundered a left-foot shot against the post and Mike Edwards had a header saved before the equaliser.