It was defender Lincoln Adams who found the net with a glancing header after a pinpoint cross from the right by Alex Callery
, while the barren scoring spell among the forwards continues.
James Ashmore had a first time 25 yard shot saved by David Campbell in the fifth minute, only for Town to take the lead two minutes later.
A corner kick from the right by Mark Robinson was headed in at the far post by Matty Tymon, and the home side thought they had struck again in the tenth minute when Kevin Burgess headed another Robinson flag kick into the net, only to have it disallowed for a foul.
It took time for Athletic to find their feet although Ryan Mallon found Brad Grayson in the 24th minute and his cross from the right was headed just over by Jack Watts
, and the visitors had appeals for a penalty turned down a minute later when Danny Walsh was bundled over in the box.
Frickley were looking more promising, Callery making space on the right in the 32nd minute and crossing for Watts to again shave the bar with a header, and Ashmore had a 25 yard volley well held by the Whitby keeper.
David Campbell made a good save from Grayson in the 48th minute before the ball switched to the other goalmouth and Andy Campbell had an effort cleared off the line by Adams.
On the hour, Callery found Watts on the left, only for him to pull his shot across the face of goal, while Billard excelled at the other end with a superb save from Andy Campbell after 77 minutes.
Frickley made a double substitution, and Leon Henry
picked out Karl Jones, whose strong shot was deflected off the line in the first minute of stoppage time.
To their credit, the visitors never gave in, and deserved the last gasp equaliser.
The man of the match awards went to Kevin Burgess and Danny Walsh respectively.
Whitby: David Campbell, Tom Marrow, Alex White, Andrew Leeson, Kevin Burgess, Michael Brough (Sam Hodgson 90+4min), Callum Martin, David McTiernan, Matty Tymon (Jake Faichney 88min), Andy Campbell, Mark Robinson; unused subs, Ashley Lyth, Darren Williams, Tom Courtney.
Frickley: Adam Billard
, Stuart Ludlam
, David Cyrus, Danny Walsh, Lincoln Adams, Michael Simpkins
, Alex Callery
, James Ashmore, Jack Watts
78min ), Bradley Grayson
(Karl Jones 62min), Ryan Mallon (Leon Henry
78min); unused subs, Kelvin Bleau, Jordan Bradshaw
Referee: Mr David Storrie