The victory moved Albion to the top of the Sky Bet Championship table - at least until the other leading teams play later ion Saturday - and extended their unbeaten run to seven matches.
Slaven Bilic's side remain the only team in the second tier not to taste defeat in the league this campaign, as they recorded their fifth Championship win.
Teenage left-back Ferguson strode forward from his own half and sent a right-footed shot past Joe Lumley at the keeper's near post and with seven minutes remaining, Pereira sealed the Baggies' win from the resulting free-kick after Barbet had been red-carded for bringing down Hal Robson-Kanu, who would have been through on goal.
Pereira, on loan from Sporting Lisbon, drilled the ball low through the Rangers wall and beyond a surprised Lumley.
Ferguson has caught the eye under boss Bilic this season and enhanced his growing reputation with a terrific performance and goal.
His all-important opener came eight minutes into the second half and was no more than Albion deserved.
They were the better side during a scrappy first half in which Charlie Austin had an effort saved by Lumley and was just unable to get to Grady Diangana's low cross.
Austin, playing against his former club as were Darnell Furlong and Matt Phillips, was given a warm reception by the home crowd before kick-off and when substituted on the hour mark.
The striker, signed from Southampton during the summer, is still waiting for his first league goal for Albion. That wait will surely not last much longer in a side with plenty of fluency going forward.
QPR, on the other hand, struggled to create clear-cut chances and rarely looked like finding an equaliser once Ferguson had broken the deadlock in emphatic fashion.
Rangers had won their previous four league games and they too would have gone top with a win, but they were second best throughout.
Ilias Chair shooting over was a rare moment of concern for Albion, who always looked threatening at the other end.
Shortly before being substituted, Austin saw a deflected shot pushed away by Lumley, who also kept out a strike from Diangana and denied substitute Kyle Edwards at point-blank range.
Lumley was unable to keep out Pereira's free-kick but did produce a fine save to prevent a third when he clawed away Robson-Kanu's header.
