With the wind in their favour, the visitors started strongly, David Bridgwater shaving the bar with a 25 yard lob in the fifth minute, and then forcing a fine save from Stephen Dickinson from a free-kick three minutes later.
Danny Walsh sent Ryan Mallon down the left for the Blues in the tenth minute, running on to head the resultant cross towards goal but his effort was blocked and cleared.
Chasetown went in front after 20- minutes, Gary Birch rising to meet a pinpoint centre from Mark Branch and head into the net from ten yards.
Grant Darley went close for Frickley with an angled drive, but the home goal had a lucky escape in the 44th minute when a free-kick by Bridgwater rattled the bar and an upright before being cleared.
It was the Blues who looked dangerous after the interval, Ben Turner producing a sizzling 40 yard drive which was only just off target in the 49th minute, while Brad Grayson chased a ball on the right and managed to cross for Ollie Ryan, whose shot was blocked.
Turner had a lob well saved by Ryan Price before Chasetown broke away in the 71st minute, Lincoln Adams tackling Dean Perrow as he shaped to shoot.
Debutant Danny South replaced Darley as the home side continued to press, James Ashmore being just off target with a first time 35 yard drive in the 76th minute and South headed wide after another piercing attack.
It was backs to the wall for the visiting defence, Ashmore having a free-kick diverted off target, while Grayson, Ryan and Walsh, all had efforts blocked as they hung on.
Frickley: Stephen Dickinson, David Cyrus, Ben Turner, Danny Walsh, Lincoln Adams, Stuart Ludlam
, Grant Darley (Danny Smith 72min), James Ashmore, Brad Grayson, Ollie Ryan, Ryan Mallon; unused subs, Mark Whitehouse
, Karl Jones, Ben Saynor
Chasetown: Ryan Price, Jack Farmer, Mark Branch, Christopher Slater, James Turner, Richard Teesdale, Mark Hands, Darren Stride, Gary Birch, Dean Perrow (Daniel Smith 82min), David Bridgwater (Lee Wright 74min); unused subs, Andrew Westwood, Carl Edwards, John Birt.
Referee: Mr Paul Cook