They kept poor Huddersfield tryless in a miserable game and moved up to sixth after confirming victory with Danny Kirmond’s 68th minute try.
It was a vast improvement on their previous outing – a 54-16 loss at home to Hull KR – and was much-needed after Trinity had also lost before that to Salford.
The turning point here came shortly before Kirmond’s try when Huddersfield finally got out of their own half after showing real steel themselves to defend three drop-outs in quick succession,
Instead of attacking, though, they opted to attempt to kick a penalty when trailing 4-2 after Ben Jones-Bishop blatantly shoved Danny Brough as the Giants captain chased his own grubber.
However, Brough was marginally wide with his effort and instead, just moments later, Wakefield captain Kirmond – back from a one-game ban –latched onto Liam Finn’s smart kick for the game’s only try.
Finn’s conversion made it 10-2 and Paul Anderson’s side, who have now lost three successive matches, never looked like recovering.
“Our kick-chase was magnificent and work off the ball won us the game,” said Chester, as Wakefield prospered at Huddersfield for the first time in four years.
“Finny kicked it very, very well but it was our best defence for some time, too. It was scrappy but we deserved the win.
“We’ve another tough game against Leeds on Friday and our points for and against is not great.
“But this now means teams below us have to win four out of five to get us out of the eight which is big ask.
“We won’t get carried away but defensively we were very good, the best for a long time, and I’m proud of the boys.”
In the first half, Huddersfield lost Aaron Murphy when the ex-Wildcats winger dived out from behind his own line to avoid conceding a second successive drop-out but suffered a nasty head wound in the process.
For a long period, in an error-ridden game played mainly in rain, neither side had enough simple control let alone guile to look like scoring a try. It would have been a big turn-off for the watching Wayne Bennett, the new England coach who has flown in from Australia for a week to spend time with his squad.
It was no surprise, then, when Wakefield’s Liam Finn accepted two points from a penalty to opening the scoring in the 26th minute.
Brough levelled with his own penalty in the 52nd minute but Finn quickly added another on and Kirmond eventually made sure.
Giants boss Paul Anderson was “very disappointed” with the loss that all but ends their hopes of gatecrashing the top eight.
But, more importantly, he and the club are praying youngster Ronan Costello pulls through after he tragically suffered a serious injury during Saturday’s under-19s game.
The teenager is in a critical condition in Leeds General Infirmary after being injured in a tackle.
Costello, 19, was taken there by air ambulance and the match against Salford was abandoned.
Huddersfield Giants: Brierley; McGillvary, Cudjoe, Wardle, Murphy; Brough, Ellis; Rapira, Leeming, Mason, Roberts, Ta’ai, Lawrence. Subs: Crabtree, Hinchcliffe, Wood, Johnson.
Wakefield Trinity Wildcats: Jowitt; Johnstone, Lyne, B Tupou, Jones-Bishop; Miller, Finn; Anderson, Howarth, England, Kirmond, Ashurst, Sio. Subs: Scruton, Arona, Arundel, Annakin.
Referee: Michael Woodhead (RFL).