Saints, who have never failed to make the post-season, came into the match on a run of three defeats in a row and five losses in six, leaving them six points off the top six.
The visitors slipped 10-0 down to fourth-placed Wakefield and trailed 16-12 at half-time but then ran in six unanswered tries in the second period.
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Tristan Sailor's brace completed his hat-trick while Lewis Murphy added to his first-half score and Jake Davies touched down twice in the closing stages to move St Helens to within four points of sixth-placed Leigh Leopards with four games remaining.
Wakefield, who lost Josh Rourke and try-scorer Isaiah Vagana to injuries inside the first quarter of an hour, missed the chance to move two points behind table toppers Leeds as they suffered a sixth successive defeat in games against Saints.
Tyson Smoothy's eighth-minute effort, which was converted by Jack Sinfield, and Vagana's Sinfield-aided score in the 12th put Wakefield on top.
However, Vagana was barged into as he went down and went off with a physio holding his left arm, after Rourke departed following a collision with Murphy.
Sailor and Murphy dragged Saints back into the contest with tries that Jackson Hastings converted, only for Sinfield to exploit a huge gap before kicking his second conversion to leave Wakefield four points to the good at the break.
Lachlan Walmsley had two tries chalked off for Trinity after the resumption, either side of which Murphy put Saints back in front with another fine finish, diving one-handed in the corner before hobbling off with an injury to his left leg.
Once Billy Keeley latched on to a loose ball and went over after 64 minutes, Saints dominated, with Sailor's hat-trick, sealed after a lung-busting run, prompting Wakefield's fans to stream for the exits.
Sky Sports will show every game of the Super League live this season, including two matches each round exclusively live. The remaining five matches will be broadcast on Sky Sports+.
