The star forward grabbed a brace on his comeback after recovering from coronavirus, as Palace scored five away from home in the Premier League for the first time.
They climbed to 11th but inflicted more Premier League misery on the Baggies, who remain in the bottom three.
Albion have won just once this season and now face the next three games without Pereira, following his dismissal for appearing to kick Patrick Van Aanholt.
Without Zaha, Palace lost to Burnley and Newcastle and he underlined his importance from the start.
First, he skimmed the bar after a fine turn and it was a warning Albion failed to heed as the Eagles took the lead after eight minutes.
He delivered a dangerous low cross and the sliding Furlong could only steer it into his own net.
It was early blow but the Baggies responded well and Pereira's sharp volley was straight at Vicente Guaita.
Furlong then thumped a header against the bar before Gallagher levelled after half an hour.
Semi Ajayi's fine pass sent Furlong clear on the right and, after his first cross was blocked, he found the unmarked Gallagher – who had a medical at Palace in the summer before they pulled out of a loan move – to sweep into the bottom corner from 16 yards.
Yet Albion's recovery fell apart just four minutes later when Pereira saw red.
The forward was bundled over by Van Aanholt and, while he was on the ground, appeared to catch the defender in the stomach with his boot.
After a VAR check, referee Paul Tierney also consulted his monitor and sent the Baggies star off.
It was a soft dismissal but Palace looked to take advantage and Gary Cahill's shot was blocked before Ebere Eze curled wide.
The first came 10 minutes into the second half as Zaha restored the Eagles' lead when he cut inside and curled beyond Johnstone from 16 yards.
Four minutes later it was 3-1 when Benteke stooped to head in Van Aanholt's cross for just his third goal of 2020.
The visitors were enjoying themselves and Zaha got a second with 68 minutes gone when he stabbed in after Eze's barnstorming run into the box.
Albion's 10 men, their confidence shot, had been blown away in the second half by impressive Palace and, after Zaha went off, they completed the rout with eight minutes left.
Nathaniel Clyne's simple pass found Benteke and he was allowed to turn in the area and find the bottom corner.