Lloyd Dean broke the deadlock just after the hour mark with a stunning bicycle kick before Dom Marie doubled their lead moments later.
Jason Mycoe lashed one in in stoppage time but it was too little too late for Albion.
Taddy boss Michael Morton made three changes to last week's FA Cup defeat to Colne as Josh Grant, Sam Akeroyd and Danny Frost were all handed starts.
On a scorching day in Costa Del Tadcaster, it was the Merseysiders who started the brighter as Harry Cain and Dom Marie both spurned half chances.
Cables then had the ball in the net but Dom Marie's glancing header was ruled out for offside.
There was little goal mouth action in the first forty five but there was plenty of questions being asked to the referee.
Aiden Savory went down off the ball in the penalty area, but Albion's appeals were waved away.
When Taddy did create some space in the final third to pull the trigger, a blue shirt was positioned well to block.
However the main talking point of the first half wasn't a piece of football but was a sending off as tensions boiled over five minutes from the break.
After a trio of full blooded challenges, you could feel that a scuffle was going to break out and that's exactly what happened as Alan Burton and Josh Grant exchanged pushes before lots of bodies piled in.
After four minutes of the officials trying to sort everything out, Taddy defender Josh Barrett was shown a straight red card for a push in the face.
Much to the anger of the Brewers bench and players.
The two main culprits of the melee; Josh Grant and Alan Burton were shown yellow cards.
Half-Time: Taddy 0-0 Prescot Cables
The dismissal forced Morton to move the versatile Aiden Savory back into central defence.
Prescot opened the scoring just after the hour mark and there was nothing that could have been done to stop it.
A cross from the left was met by an incredible overhead kick by Lloyd Dean from just inside the penalty area.
The lead was then doubled six minutes later when Dom Marie burst down the left, cut in-field and fired into the bottom corner to leave Albion with a mountain to climb.
Taddy continued to plug away however but as they ventured more bodies forward for a way back into the contest, Prescot tried to make absolute sure.
Substitute Tunde Owolabi was put clean through on goal seconds after entering the field but goalkeeper Michael Ingham produced an outstanding save to tip over the bar.
From the resulting corner Owolabi was denied by Ingham again as his header was beaten away.
Taddy did manage to pull a goal back in stoppage time as substitute Jason Mycoe lashed in from a corner.
It was just too late to try and salvage a point though as Prescot saw out the victory.
Full-Time: Taddy 1-2 Prescot Cables
Taddy: Ingham, Hardy, Grant, Sellars (Crouz 70), Milne (c), Barrett, Murray (Mycoe 78), Akeroyd (Roper 61), Corner, Frost, Savory
Unused: Dixon, Stewart
Prescot: Burgess, Scarisbrick, Fernandes, McCulloch, Herbert, Conte, Faux, Burton, Marie, Dean, Cain
Subs: Coyne, Owolabi, Southworth, Wright, Wynne