
Michael Donohue's stunning opener had given Neil Reynolds' men the lead but Fewster's leveller in the first half at Broadhurst Park - a venue that has seen some classic encounters between the Red Rebels and the Seasiders - ensured Nathan Haslam's side maintained their unbeaten away record.
Town looked bright early on, albeit without creating anything clear cut until the 15th minute when Fewster headed narrowly over the bar following Jacob Gratton's exquisite cross.
Junior Mondal almost produced an opener when his strike after cutting in from the right, was drilled just wide of the Pat Boyes' left-hand post.
But they fell behind after 23rd minute. A fantastic first-time strike from distance by Donohue flew past Shane Bland before he had chance to react, opening the scoring for FC United of Manchester.
The host's tails were now up and they continued to pose a few questions for the Seasiders' backline, with Max Cane firing over the crossbar before Whitby were able to settle down and create some openings of their own.
After having one goal disallowed following a tight offside call, though, Whitby did find an equaliser. Fewster, the man who was denied minutes earlier, capitalised on a poor back pass from Guy Hall and accelerated around 'keeper Boyes to fire a right-footed shot into the empty net - much to the delight of the travelling contingent.
After the break, chances came and went for both sides, but it always looked like Haslam's men would snatch the win if anyone was going to come away with all three points.
Jay Fitzmartin, however, would give Town a scare when a long ball forwards allowed the attacker to beat Adam Gell for pace but he could only fire high over the bar from a difficult angle.
Just after the 70 minute mark, experienced midfielder Lewis Hawkins forced FC United's shot-stopper into a save as Boyes tipped his effort over the bar with a fingertip save.
But even when Boyes was second favourite, Whitby still couldn't find that winning goal. Gratton could and should have scored minutes later, but he got it all wrong in front of goal, slashing an effort high and wide from close range.
Substitute Aaron Haswell was denied by a smart low stop from Boyes, before Gratton would hit the target, only to be prevented from firing home by the in-form goalkeeper.
It looked as if Whitby would snatch all three points in stoppage time when Mondal timed his run to perfection, latching onto Alfie Doherty's through ball. After rounding Boyes, Mondal was denied by a heroic last ditch block from a defender.