Trinity deserved their third win in four matches since Poching took charge through their second half performance, though Leeds had led twice in the game.
Rhinos had more to play for - and an extra day’s rest - but looked the more tired side and weren’t able to build any pressure after half-time.
Watched by a crowd of 5,420, Leeds were six points ahead at the interval, two of the three tries coming in the final six minutes of the half.
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Though Wakefield had more of the territory, Rhinos created the clearer chances and were generally solid in defence, particularly when they were down to 12 men - something they have had an alarming amount of practice at.
The first of Rhinos’ almost inevitable sin-binnings came early on, captain Matt Prior being banished for a high shot on Innes Senior after just five minutes.
The second was 15 minutes from time when Prior went again following a punch-up, this time being joined by Trinity’s Chris Green.
A big factor in the second half were the penalties, all four of which went Wakefield’s way, after they had been split three-each in the opening 40.
It was a game where nobody particularly stood out, though Eddie Battye and Kelepi Tanginoa were good for the hosts and Kyle Wood also had some effective moments.
Halves Jacob Miller and Mason Lino troubled the visitors with their kicking at times, but also took some wrong options.
Try scorers Brad Dwyer and Kruise Leeming played well for Rhinos, as did Rob Lui and Rhyse Martin, but Leeds’ attack is not firing at the moment and they made some weary errors, under pressure, late in the game.
They were fortunate rivals Castleford Tigers, Hull KR and Hull all lost, so Rhinos ended round 22 where they began it, in fifth place.
Leeds were a man down when they opened the scoring after 14 minutes, totally against the run of play.
It came from good work initially by Dwyer to charge down Lino’s kick.
He gave the ball to Leeming - again starting in the halves - who shipped on to Ash Handley.
The winger was tackled, but on the next play Tom Briscoe’s pass found Leeming and he cruised over for a try which Martin converted.
Dwyer made a terrific break soon afterwards and was later held up over the line from acting-half and on the half hour Cameron Smith also crossed the whitewash, but lost possession.
Other than that, Trinity did most of the pressing, but a lack of composure and some strong defence forced them into a succession of errors in good field position.
Leeds looked to have weathered the storm when Trinity levelled six minutes before the break.
Lee Kershaw had a good run, then Jordan Crowther was tackled just short, but Miller engineered an opening for Tanginoa on the next play and Lino added the extras.
Rhinos, though, struck in the closing moments of the half to go in at the break ahead.
Lui kicked low between the posts and - in similar fashion to his try against Wigan last week - Dwyer ran through to gather and touch down, after Dave Fifita and Lino had failed to tidy up.
It was Dwyer’s 11th try of the season and sixth in Rhinos’ last seven games.
Martin’s second goal made it 12-6, but Trinity levelled in similar fashion 12 minutes after the break and looked the more likely winners from then on.
Dwyer and Tom Holroyd did very well to prevent Miller grounding the ball over the line, but then Wood’s kick deflected off a post, which fooled the defence and Cowther touched down.
Lino converted and Tom Johnstone made an outstanding tackle to prevent Rhinos regaining the lead, barging Luke Briscoe into touch just short.
Moments later Leeds’ defence let Miller’s kick bounce, Lino picked up with support outside him, but his pass was intercepted by Callum McLelland. Handley did the same soon afterwards.
The penalty after the double sin-binning went to Trinity and that paved the way for Miller to boot a one-pointer.
A mistake by Battye from the restart handed the ball straight back to Rhinos and Lui knocked over a drop goal to level.
Golden point loomed at that stage, but Ryan Hampshire kicked Trinity back in front in similar style with six minutes left and in the final moments, after Richie Myler spilled a kick, Joe Arundel crashed over to seal it and Lino converted following the hooter.
Rhinos’ only change from the win at Wigan was substitute McLelland’s return to the 17 in place of the rested Morgan Gannon, with James Donaldson stepping up off the bench into the starting second-row.
The luckless McLelland was available after illness, but hobbled off in clear pain in the final stages.
Green started for Trinity despite not being named in their initial 21. In normal circumstances, that would have cost them an interchange, but - as it was Covid-related, Tinirau Arona having tested positive - there was no forfeit.
Arundel also came into the team, with Joe Westerman and the injured Matty Ashurst dropping out.