Wakefield led 10-0 with tries from Semi Tadulala and Oliver Elima before Solomona limped off after 20 minutes.
Richard Whiting and Kirk Yeaman crossed to give Hull a half-time lead, and Garreth Carvell adding another after the break to extend the advantage.
Tadulala and Jason Demetriou went over for Wakefield but Hull won it with tries by Paul King and Gareth Raynor.
Hull coach John Kear: "I said earlier in the week that I would rather an ugly performance and a win than a pretty performance and a loss.
"It puts us back in the shake-up for where we want to be and that's looking at the top of the table.
"We had lost three on the trot and our confidence was bound to be fragile. The players wanted to get back on the horse and they have done."
Wakefield: Halpenny, Buchanan, Henderson, Demetriou, Tadulala, Rooney, Obst, MacGillivray, March, Catic, Solomona, Elima, Betham. Replacements: Griffin, Korkidas, J. Field, White.
Hull: Briscoe, Dixon, Domic, Yeaman, Raynor, Cooke, R. Horne, Thackray, Brough, King, Chester, Radford, Whiting. Replacements: Tony, Lupton, Wheeldon, Carvell.
Referee: R Silverwood (Dewsbury).
MMIX
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