The Blues suffered back to back defeats under player-boss Gary Liddle for the first time, after a loss on Saturday.
Whitby dropped three places while Workington leapfrogged them after a deserved win in this coast-to-coast clash.
The hosts could have led inside 2 minutes as Stephen Walker, but Town's top scorer could only fire over from a tight angle.
To compound their frustration, the Cumbrian visitors then went ahead themselves within five minutes.
There was controversy on 32 minutes when the Workington keeper took out Layton Watts just outside the away box, but escaped with just a yellow card.
He was on hand, seconds later, to tip away Nathan Thomas' goalbound free-kick, which was headed for the roof of the net.
At the other end, Henry Popple saved well in first half stoppage time.
Early in the second period, the visitors weren't to be denied, six minutes into the restart, beating Popple to double their advantage.
The away side put the game beyond doubt as they made it 3-0, 15 minutes from time.
Popple did well to block a powerful effort from distance, with sub Matty Tymon heading inches wide for Whitby at the other end, from Thomas' cross.
Tymon did eventually find the net, with a low drive from a loose ball, with five minutes left. But it proved a mere consolation.
Liddle spoke to Whitby Town TV after the game:
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