Not in the contest for the opening 39 minutes, Wildcats, inspired by scrum-half Tim Smith, turned the game on its head in an eight-minute spell which yielded three converted tries.
From 16-0 down, the visitors suddenly found themselves two points ahead, but they were unable to go close the game out and were pipped 34-26.
Both teams knew victory would be a giant step towards retaining their Super League status, particularly after Leigh Centurions – the Championship team with the best promotion credentials – lost their opening game at home to Hull KR.
In an increasingly frantic encounter, the teams swapped tries, but it was Wakefield who held the upper hand when they led 26-22 with barely 10 minutes left.
At that stage Smith’s pass created an opening for centre Bill Tupou, who had his winger Richard Owen in support.
Had Tupou passed, Owen would only have had to make the catch to score what could well have been a clinching try.
Instead he went himself and was tackled.
On the next play, Scott Moore kicked to Rangi Chase and the Salford stand-off raced the length of the field to cross between the posts.
The third of Josh Griffin’s four goals edged Salford back in front and they sealed a priceless win in the final moments, when Cory Paterson touched down from Michael Dobson’s kick.
Wakefield effectively lost the game with a passive first-half performance, which saw them carry the ball into the hosts’ 20-metre area only twice, the first time after 37 minutes.
By that stage Salford were 16-0 ahead. Their first try was a stunning effort by Josh Griffin, who gained possession 40 metres from his own line, burst past the first line of defence, skipped round Lee Smith and then held off the full-back’s second attempt for a dazzling eighth-minute touchdown.
Eight later he added a second from Ben Jones-Bishop’s offload, after Michael Dobson had moved play left.
On the half hour the home team tapped back-to-back penalties in front of Wakefield’s posts, which was a measure of how much they felt in control and from the second of those George Griffin rumbled over.
Wakefield scored on the final play of the first half to give themselves a glimmer of hope. Owen made a strong run, Tim Smith kicked ahead and regathered and Jacob Miller was on hand to take the pass and stretch over.
The first of Lee Smith’s five goals made it 16-6 at the interval and Wakefield were in front eight minutes afterwards, Miller and then Danny Washbrook both crossing off exceptional passes by Smith.
Paterson went over following back-to-back penalties for a try which he also converted, but then Miller intercepted a Chase pass, kicked to the corner and Reece Lyne ran through to touch down.
Smith added a penalty to open a four-point gap and at that stage Wakefield seemed the most likely winners.
In a cryptic post-match press conference, coach Brian Smith appeared to point a finger at referee James Child, whose penalty count finished 8-5 in Salford’s favour.
Smith did not mention Child by name or directly refer to the officials, but he claimed: “It wasn’t all together to do with how we played, there was plenty of other stuff today.
“We played against a team that was faultless virtually.
“They also managed to get through the half without conceding a penalty, which I reckon is a tall order – very, very clever,” he said.
“It is very, very hard to play when you feel like you’re the ‘B’ team in a training game.
“When you play at training, the ‘B’ team does just what the ‘A’ team wants them to do. We referee it that way so that all the things are manufactured so we can practice exactly what we want to do.
“Salford played as the ‘A’ team for the first half. As soon as things changed, we changed.
“We changed and things changed, there was a bit of both. As soon as we got into that ‘A’ team opportunity and executed like we can, they couldn’t hold us,” he said.
“Then we didn’t finish that job off.”
Salford Red Devils: Jones-Bishop, J Griffin, Thornley, Sa’u, Johnson, Chase, Dobson, Taylor, Tomkins, G Griffin, Hansen, Maitua, Paterson. Substitutes: Lee, Krasniqi, Evalds, Morley.
Wakefield Trinity Wildcats: L Smith, Owen, Tupou, Arundel, Lyne, Miller, T Smith, Scruton, Moore, Anderson, Molloy, Ashurst, Simon. Substitutes: Sio, Walker, Mullally, Washbrook.
Referee: J Child (Batley).