Tau started from the substitutes' bench once again, as the Seagulls aimed a return to winning ways to ease their relegation fears following a four-match winless run across all competitions.
West Brom were up and running 11 minutes in from a pin-point header by Kyle Bartley following a corner-kick by Conor Gallagher.
Graham Potter's side had a chance to go level four minutes later as an outstretched arm from Okay Yokuslu led to a penalty following a Video Assistant Referee (VAR) review, but Pascal Gross missed.
The Seagulls looked to have gone level on the half-hour mark from a low free-kick outside the area by Lewis Dunk, but it was disallowed following a VAR review.
A re-take was ordered instead and at the second time of asking Dunk failed to get the better of goalkeeper Sam Johnstone, who smothered quite easily.
Brighton still continued to threaten the equaliser on the stroke of halftime with a smart attempt from Aaron Connolly after cutting inside, but Johnstone expertly parried the effort.
In the second half, Brighton made the first substitution of the match in Adam Lallana who came in for Alexis Mac Allister.
The Seagulls should've gone level minutes in from the break after Johstone parried a shot from Neal Maupay back into the path of Connolly, who blazed over from close metres.
West Brom gave away another penalty in the latter stages when Gross succumbed to a foul in the area by Conor Townsend, however Danny Welbeck failed to capitalise.
The Baggies weathered the storm in the closing minutes to stretch the visitors' winless run and rekindled their survival hopes.