Salford scored first in each half, but other than that the visitors were the better team.
Their second-half effort was particularly impressive, a spell of three tries in 13 minutes sealing the victory.
Chester said: “I thought we were good value, we stuck to the plan really well. It was a scrappy game in the first 40 minutes, but in the second half we completed at 93 or 94 per cent and that kind of ball control generally wins you games.
“We were excellent in that second half and that needs to be a minimum standard now moving forward. We know when we play error-free footy we are a hard team to beat.”
Wakefield’s 6-4 half-time lead could have been greater on balance of the limited chances. They recovered well from going 4-0 down after 15 minutes to a try inspired by their old boy Pauli Pauli. The massive forward got a terrific offload away to Kris Welham and he supplied Tui Lolohea who crossed off a one-two with Ken Sio.
Trinity had already gone close through Jay Pitts and grabbed the lead on 25 minutes when the lively Kyle Wood sent Reece Lyne into space and Max Jowitt was in support to cross. Jowitt is a specialist full-back, but started at stand-off, becoming Jacob Miller’s third half-back partner in four games.
In the next set Ryan Atkins split the defence, but full-back Alex Walker dropped the pass.
Pitts got over the line in the final seconds of the half, but was held up.
Other than the try, Salford’s only opportunity came following a powerful run by Pauli, but Joey Lussick was pulled down when he darted from acting-half.
Salford regained the advantage six minutes into the second period through Sio, who got over at the corner from Niall Evalds’s pass. Lolohea could not convert – for the second time – and Trinity were back in front within six minutes when Tom Johnstone went over after Salford’s right side defence failed to deal with Jowitt’s kick.
Bill Tupou had a strong game and widened the gap with an airborne finish from Reece Lyne’s pass on 58 minutes, then with 15 left Kelepi Tanginoa secured the ponts and capped a big individual performance by charging over from Miller’s pass.
Sio pulled an unconverted try back with eight minutes remaining, in similar fashion to his first score, but Trinity weren’t threatened in the closing stages. Chester said: “It is always a tough place to come, we haven’t had a great deal of success here so it’s nice to go two wins from four games. I am delighted for the team, the guys were outstanding.”
Salford Red Devils: Evalds, Sio, Welham, Sarginson, Williams, Lolohea, Atkin, Mossop, Jones, Dudson, Pauli, Roberts, Yates. Substitutes: Lussick, Lannon, Ikahihifo, Flanagan.
Wakefield Trinity: Walker, Tupou, Lyne, Atkins, Johnstone, Jowitt, Miller, Kopczak, K Wood, Navarrete, Ashurst, Pitts, Westerman. Substitutes: J Wood, Green, Tanginoa, Crowther.
Referee: L Moore (Wigan).