Sam Williams kicked Trinity into the lead with a penalty on five minutes and after great work from the visitors, Mason Caton-Brown forced his way over for a try on his debut midway through the first half.
Williams added the conversion and he made it 10-0 seven minutes later with a penalty.
Saints finally responded five minutes before the break when Ryan Morgan crossed to put them within six points at half-time.
The home side turned the screw at the start of the second period and were rewarded with two tries in eight minutes from Mark Percival to edge them into a 12-10 lead.
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However, Wakefield weren’t finished and they won it seven minutes from time when Jacob Miller was awarded a decisive penalty try after he was held back by Richardson.
Williams added the conversion and the visitors held out to claim the points.