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Bradford thought they had hit back when Danny Addy crossed, but his score was chalked off for an inadvertent knock-on in the build-up.
The Wildcats were then denied a second try soon after for a forward pass before Joe Arundel failed to convert a penalty.
Early in the second half, Wakefield looked to be out of sight when Anthony Mullally crossed for his second try of the post-season.
On 54 minutes, the Bulls pulled to within two points as Matty Blythe dived over the whitewash.
Just after the hour mark, Danny Washbrook broke through the line to increase Trinity's lead before Purtell touched down to keep the visitors in touch.
Addy missed a penalty kick, which would have brought the scores level, but a late Scott Moore try ensured that Wakey retain the place in rugby league's top flight for another year.