Leigh finished the game with 11-men with Brierley and Rob Butler sin binned but held on to claim just a second win of the Betfred Super League campaign.
In his programme notes Beaumont had slammed his side’s second-half collapse against Hull KR at Magic Weekend as “absolutely disgraceful and weak.
He added: “It was a complete collapse, a surrender of belief and desire and will to give pride to the situation. I felt hurt by it and still do.
“Do I care what response I get as a result of them reading this? Not at all as they can decide what history they want to be part of and how they represent themselves.”
His stinging rebuke struck an early chord as Leigh set about ending their home campaign on a positive note.
There was no lack of effort as prop Adam Sidlow crashed over after 10 minutes and Brierley followed up Jack Logan’s kick to register his landmark try five minutes later. Brierley added one conversion to put Centurions 10-0 in front.
However, Kurt Haggerty’s men have imploded too often this season and three tries in 14 minutes put the visitors in command.
Reece Lyne followed up his own kick to touch down after 20 minutes while Kelepi Tanginoa and David Fifita crashed through some suspect defence to wipe out Leigh’s advantage.
Mason Lino improved all three tries to put Trinity 18-10 in front and they should have scored again before half-time but Lee Kershaw, James Batchelor and Lyne contrived to spurn a glorious opening on Leigh’s left flank.
It was almost winger Kershaw’s last involvement before he was helped off after a heavy tackle.
Centurions’ forward Nathan Mason suffered an even heavier knock in the last play of the half.
The former Huddersfield and London Broncos prop received lengthy on field treatment during the interval before being carried off on a stretcher.
Referee Rob Hicks put the incident on report before the teams resumed the final 40 minutes.
Leigh were again quick out of the blocks. Centre Iain Thornley broke down Trinity’s right and Brierley backed up to claim his second try.
He completed his hat-trick after 55 minutes and goaled both to edge Leigh into a 22-18 lead.
Wakefield tried to hit back but referee Hicks disallowed possible scores for former Leigh favourite Liam Kay and Batchelor (twice).
So, when recent Australian signing Sam Stone grabbed his first try with 13 minutes left, Centurions took a vital two score lead, a valuable buffer when Butler was yellow carded for use of the elbow and Brierley for a professional foul.