The Red Devils full-back scored at the start of the first half and the end of the second while Andy Ackers also touched down for Paul Rowley’s men. Scrum-half Marc Sneyd kicked four goals from as many attempts as Wakefield were nilled for the sixth time this season.
The win cements Salford’s play-off place with only four rounds of the regular season remaining. But it is a different story for Wakefield who remain two points adrift of 11th-placed Castleford.
Despite being nilled for the sixth time this season, Applegarth refused to be too critical of his players, although he was frustrated by critical, individual errors.
“Some of the lads put in unbelievable defensive efforts,” said Applegarth. “Salford’s tries were pretty soft but we came up with that many unforced errors… we can’t keep on saying this.
"We are running out of time and we need to sort it out. We have some honest conversations to have about it this week.
“Some of those errors tonight I wouldn’t expect from an academy team, let alone a Super League team. There’s going to have to be changes next week.
“There’s no point shying away from how you feel after a tough loss like that. I hope people are hurting in our dressing room because it shows how much it means to them. We need to dust ourselves off and get ready for St Helens next week.
“I have said all along that I will never question the lads’ fight and attitude to play for the club and we still showed that tonight.
"The defensive resilience is exactly what we need to base our game on. As a team we can’t afford individual mistakes."
Trinity trailed from the fourth minute and barely created a scoring opportunity as they looked for only their fifth win of the season.
Will Dagger returned from injury for Wakefield who had centre Reece Lyne making his 250th career appearance.
Brierley’s early try was converted by Marc Sneyd, who also kicked a first-half penalty.
Salford added a second try in the 49th minute when Wakefield’s attempt at a short goal-line drop-out went badly wrong and the ball sat up for Andy Ackers who charged over from close range. Sneyd’s third goal made it 14-0.
Salford sealed victory when Brierley scored his second in the 78th minute – supporting a break from Ken Sio after he intercepted a stray pass on his own 20-metre line. Sneyd added the goal to make it 20-0.
Wakefield’s dismal night was compounded by an injury to full-back Max Jowitt who limped off.
With only four rounds of the season remaining, Applegarth’s task is made all the more difficult by fresh injuries to Jowitt and Lyne.
He said: “For Max, we will have to see how he settles down. Reece has done his hamstring so we will see how that settles down over the next few days.”