Goals from Matty Tymon and Layton Watts put the Blues ahead at Rushall, only to twice be pegged back.
Tymon had given the visitors an early lead after Jake Charles' shot was blocked and the big frontman followed up for his fourth goal in five games.
However, the hosts levelled and had the better of the first half.
Undeterred, Watts put the Seasiders back in front, after the interval, latching onto sub Harley Dawson's neat ball forward before flicking home.
But Olympic levelled once again to claim a share of the spoils.
Skipper Lewis Hawkins played his 200th game for Whitby Town and spoke to Whitby Town TV after the game:
Co-manager Jason Kennedy was also satisfied with a point:
The Blues remain seven points clear of the relegation places, they've lost just one of their last seven matches.
They host Lancaster City, in NPL Premier, next Saturday.


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