Hull brought things back on level term just after the half-hour mark when Tom Lineham made the most of a Wakefield mistake to go over.
It was the visitors who went into the break ahead, however, as Oliver Wilkes touched down just before half time to make it 16-10 to Wakefield.
The topsy-turvy nature of the match continued in the second half as Hull once again restored parity through Crooks, who ran the length of the field having scooped up Tim Smith's attempted grubber kick.
Hull then took the lead as Crooks completed his hat-trick when the video referee awarded him a try in the corner.
Once again the momentum switched soon after, however, as Wakefield touched down twice in quick succession - through Smith and Fox - to regain the lead.
Kirk Yeaman equalised with six minutes left, scoring a try to make it 26-26, but Danny Tickle couldn't add the vital extra two points with the conversion.
Smith then knocked over a drop-goal for the visitors with a minute to play, giving them a 27-26 lead, before Hull's attempted drop-goal to draw level was charged down, handing Wakefield a dramatic win.