Two second-half tries from the Warriors proved key as Marshall scored straight from a 20-metre restart before Sam Powell sealed the visitors’ success late on.
The decision to award Marshall’s third score of the afternoon angered Trinity boss Chester who felt the four-pointer should have been chalked off.
The Wigan winger appeared to take the tap to begin the 20-metre restart a good few metres away from the centre of the 20-metre line.
The try put Wigan 18-12 up after the sides had been locked in a tight contest for nearly an hour.
Marshall pouched a kick in the in-goal and raced to take the tap before easing through the hosts’ defensive line and racing clear to score.
“I can cop a player being a metre away from the centre spot but when you are talking six or seven metres, I don’t know how many officials there is there,” vented a frustrated Chester.
“You have got a bloke behind the posts – I don’t know what his job is – you have got a referee that is on the spot and just let Liam Marshall tap it wherever he wanted.
“That is just a disgraceful call and the calls that you shouldn’t get wrong.
“There is a line there to tell you where to tap the ball.”
Trinity played more than half the match with just two interchanges after Bill Tupou and Chris Annakin were forced off through injury.
Tupou suffered a suspected injury to his pectoral muscle while Annakin has sustained a groin strain.
And Chester doesn’t expect the pair to play any further part this season.
“I thought it was a bit of deja vu, when we played Wigan down here last time we lost all the bench just after half-time," he said.
“So we did it the tough way, Bill looks like he has done his pec and Chris Annakin a groin, and they don’t look great.
“We have got some cover there with Joe Arundel, George King and Jordan Crowther so we have pretty much got that covered.”
Loose forward Kelepi Tanginoa was moved into the vacant centre spot following Tupou’s departure and dragged Trinity back into the game with a fantastic break.
Wakefield were 12-0 behind after 30 minutes but Tanginoa’s break eventually led to a try for Jacob Miller, just after James Batchelor had got Trinity on the board.
Two tries from Marshall and a penalty from Zak Hardaker saw the sides go in level at the interval.
Trinity’s only score of the second half was a well-taken try from Ben Jones-Bishop, from Morgan Escare’s kick. That was sandwiched between Marshall’s hat-trick score and Powell’s last-minute effort.
“He was outstanding,” said Chester of Tanginoa’s display.
“He played three different positions out there, I thought he looked great in centre and has given me some food for thought.
“He was by far and away the best player on the field today and he played for 80 minutes.
“He played the first 30 minutes in the middle and then in the back-row and then moved into the centre for us.
“I haven’t got a bad word to say about the rest of the guys and we didn’t get beat on effort.”
Despite the disappointing nature of the defeat, Chester was full of pride after his players battling display.
Wigan have now won 10 of their last 11 games and, according to the Trinity chief, are the best team in Super League at the moment.
“I couldn’t be prouder of the players today,” added Chester.
“They are the best team in the competition at the moment and I thought we more than matched them.”
Wakefield travel to Warrington Wolves on Friday night before ending the season with a home clash against London Broncos.
The Broncos’ 36-10 defeat to Leeds Rhinos will have come as a welcome result to many at Belle Vue, although Chester feels Trinity still need one more win to secure survival.
“It is all in our hands, there are three teams on 20 points,” said Chester.
“I think we need another win and hopefully we can get it over the next two weeks.”
Wakefield Trinity: Escare, Jones-Bishop, Lyne, Tupou, Hampshire, Miller, Brough, England, Wood, Kopczak, Kirmond, Batchelor, Tanginoa. Subs: Randell, Annakin, Green, Tangata.
Wigan Warriors: Hardaker, Marshall, Sarginson, Gildart, Burgess, Williams, Leuluai, Clubb, Powell, Partington, Isa, Farrell, Smithies. Subs: Greenwood, Navarrete, Byrne, French.
Referee: Scott Mikalauskas.