Albion saw Mbaye Diagne's goal questionably ruled out by VAR early in the first half at the Hawthorns.
But Sam Allardyce's side recovered from that blow to sweep into a two-goal lead by half-time thanks to Matheus Pereira's penalty and a Matt Phillips strike.
Callum Robinson sealed West Brom's second successive win after the interval as the Baggies built on their stunning 5-2 victory at Chelsea.
Second bottom Albion move within eight points of fourth bottom Newcastle with seven games left.
The Baggies have scored eight goals in their last two games, two more than they had netted in their previous 11 combined, but their unexpected revival might have come too late to save them from slipping into the Championship.
"We have had two very important wins that are pricking up people's ears but unfortunately we have to rely on other people losing," Allardyce said.
The latest VAR row in a season of problems with the technology drew a scathing response from Allardyce.
"I'm afraid so," he said when asked if VAR is a laughing stock. "There are too many of us not being given an opportunity to express how to make it better."
At the Amex Stadium, Everton was hoping to close the gap on fourth placed West Ham in the race to qualify for next season's Champions League.
But Carlo Ancelotti's team managed only one shot on target as its winless run extended to five games in all competitions.
Brighton dominated for long periods and Neal Maupay and Yves Bissouma, with a spectacular overhead kick, both went close in the first half.
Lewis Dunk's goalbound flick brought a fine save from Everton keeper Robin Olsen after the break.
Maupay and Jakub Moder were narrowly off target as Brighton pressed for a winner.
But Alex Iwobi nearly snatched the points for Everton when he flashed his shot wide in the last minute.
Everton, in eighth place, is seven points behind West Ham with a game in hand, while Brighton moved seven points clear of the relegation zone.