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Three tries in the space of 10 first-half minutes by Micky Higham, Sam Hopkins and Ben Crooks had put Leigh in control.
But Tom Johnstone, Jacob Miller and Ben Jones-Bishop crossed to turn the game around for the hosts after the break.
Leigh saw a second-half score for Matty Dawson ruled out for a forward pass.
Had Ryan Hampshire's long floated pass to Dawson not crept ahead of play, Leigh could have stretched their lead to 12 points going into the last quarter.
But within two minutes, a clever grubber from Wakefield scrum-half Liam Finn allowed Miller to score under the posts and level the scores.
Sam Williams then executed a pin-point cross-kick for Jones-Bishop to collect out wide and, after the video referee eventually awarded a try, Wakefield reclaimed a decisive lead.
Trinity's third victory of the season takes them level on points with Leigh, who have now lost four matches away from home.
Wakefield coach Chris Chester: "It was a tale of two halves. We looked in control after 23 or 24 minutes, but then came up with a poor play and we struggled to contain them.
"We need to be a lot better defensively because we conceded some really soft tries, a couple of dive-overs.
"But I'm pleased with the way we stuck at it and I thought we were worthy winners.
"We were a totally different team in the second half, very dominant, I thought we got back to where we were a couple of weeks ago.
"I'm proud we got the two points but we're certainly not getting carried away."
Leigh coach Neil Jukes: "I'm just really disappointed with our second-half performance. We were like chalk and cheese.
"For 40 minutes we were on fire and, if we'd have had a half-decent second half, I'd have thought fair play, but we were garbage in the second half.
"We lost (Josh) Drinkwater but that's no excuse for trying to cling onto a 12-point lead.
"I'd like to have given the guys a long weekend off and kick on on Monday but we'll be in tomorrow and we'll fix it up.
"We've got to find that away form."
Wakefield: Allgood, Arona, Arundel, Ashurst, Batchelor, Fifita, Finn, Grix, Hadley, Hirst, Huby, Johnstone, Jones-Bishop, Kirmond, Miller, Tupou, Walker, Williams, Wood.
Leigh: Naughton, Brown, Higson, Crooks, Dawson, Drinkwater, Hock, Higham, Weston, Hansen, Pelissier, Tickle, Vea, Hampshire, Reynolds, Green, Hopkins, Acton, Burr.

A BBC team and some tourists were on the volcano when the explosion happened.
BBC science reporter Rebecca Morelle described the experience of "Running down a mountain pelted by rocks, dodging burning boulders  and boiling steam" and says they had "a very narrow narrow escape".
The emergency services thankfully got everyone off the mountain safely with no serious injuries.
Rebecca Morelle said a volcanologist who was there at the time had told her it was the most dangerous incident he had experienced in his 30-year-career.
Lava flow mixed with steam had caused a huge explosion, which pelted the group with boiling rocks and steam, she said.
Mount Etna is one of the most active volcanoes in the world, it's been erupting for the last three weeks.
Mount Etna erupts a few times a year.
Wakefield scored three second-half tries as they came from behind to beat Leigh Centurions and deny the visitors a first Super League away win.
[NEXT_CONCEPT]
Mount Etna on the Italian island of Sicily has erupted.