Warrington started this home Cup tie as clear favourites to beat Wakefield at home and book a date to welcome Wigan to the Halliwell Jones Stadium in the quarter final. The bookies had them at 10-3 on for the win, while Trinity were 5-2 - despite beating their hosts in the league last weekend.
The Wolves were hit by a number of absences, though, most notably full-back Stefan Ratchford, who was replaced by Josh Thewlis.
But they did welcome summer Australian signing Billy Magoulias into the team for the first time, starting from the subs' bench. Josh Charnley also returned to the Warrington wing following a two-match suspension.
The Wolves had the best of the opening exchange, restricting Trinity in defence and getting near to crossing in attack, before handing the ball over just in front of their opponents' try-line.
With just three minutes of the game gone, they had the afternoon's first penalty as Wakefield were caught offside and started their next attack from just 20m out - but it came to nothing as the Trinity defence numbered up and pushed them into touch.
The hosts did open the scoring with nine minutes gone when Gareth Widdop broke the line and ran through before the defence caught up with him. From 20-plus metres out he kicked ahead and to his left for Connor Wrench to run onto the ball and touch down under the posts. The conversion was a formality for Widdop.
The Wolves scored their second in two minutes when full back Thewlis ran through the line in his own half and raced clear to touch down. Widdop's second conversion gave the Wolves a 12-0 lead with 12 minutes on the clock.
Trinity started to get properly into the game as it approached the 20-minute mark and came close to scoring on the right wing, only for Reece Lyne to lose the ball forward inches from the line.
In the next set, though, the Wire showed their threat when George Williams raced 30m from a scrum in their own half and but at the end of the set, Charnley batted a kick back to Peter Mata'utia, who couldn't control it and knocked on himself with the line backoning.
It was Wakefield who scored next, moving the ball rapidly to their left for Lewis Murphy on the wing to cross for his debutant professional try.
Mason Lino kicked the conversion from the touchline to halve Warrington's lead at 12-6.
Warrington started to look frustrated by that score, throwing poor - or non-existant - offloads which kept the advantage with Wakefield who kept up the pressure in attack and defended well when Warrington got near their line.
But they couldn't transfer that pressure into points and with the hooter looming Warrington looked like they would extend the lead when Gorge Williams crossed the line, only for play to be called back for an incorrect play the ball.
Wakefield seemed to have their own chance to score on the hooter when Kay got on the end of of a kick to right wing and hacked the ball into the in-goal area. But the play - and the half - ended in controversy when the chasing Kelepi Tanginoa looked to be tackled without the ball by the Warrington defence.
Referee Liam Moore refused to take a second look at the incident, or award a penalty, though – and the half ended.
The game resumed after the break in the same pattern: Warrington making good individual runs, but Wakefield teamwork producing sold defence and attacking pressure.
The teamwork payed off on 57 minutes when Lino passed the ball out to Liam Kay on the right wing. He passed back inside to Reece Lyne who broke through two Warrington defenders and ran 30m to touch down by the posts. Lino converted to level the scores at 12 apiece.
Two minutes later Corey Hall crossed on the left wing after a looping pass from centre field. Lino couldn't convert, but Wakefield led for the first time in the match, with 60 minutes gone, at 12-16.
Trinity continued to press for the next 10 minutes without adding to the score, but as the clock moved into the final 10 the pressure mounted for both sides, with Wakefield forcing a dropout and Lino crossing to be held up.
Wire pressed too without getting to the line, with desparate offloads moving the ball around the team but not producing a score.
When another loose offloaded gave Trinity the ball in the final minute, the visitors had posession during the final set of the tie and duly held on to book that quarter-final against Wigan.
The Wolves had been looking for a bounce-back after last week's loss and for the opening period it looked they might deliver one.
But as the game went on Wakefield's teamwork began to dominate - although half-back Lino produced his own match-winning turn, constantly teasing a defence who had no answers to his movement, passing and kicking.
Full Time: 12-16
Half Time: 12-6
Score Progression: 4-0, 6-0, 10-0, 12-0, 12-4, 12-6. HT. 12-10, 12-12, 12-16
Warrington Wolves: Thewlis (T), Charnley, Mata'utia, King, Wrench (T); Widdop (2G), Williams; Mulhern, Walker, Cooper, Currie, Robson, Holmes. Subs: Philbin, Clark, Magoulias, Davis.
Wakefield Trinity: Jowitt, Kay, Lyne (2T), Hall, Murphy (T); Miller, Lino (2G); Arona, Hood, Tanginoa, Ashurst, Pitts, Crowther. Subs: Battye, Batchelor, Whitbread, Aydin.
Referee: Liam Moore
Venue: Halliwell-Jones Stadium, Warrington