Pereira finished with two birdies at Trump National. He was as hot at the end of his round as Varner was cold. Varner, who had the 18-hole lead, had two bogeys with no birdies on the back nine to fall out of the lead with a 72.
Pereira signed with LIV Golf at the start of this year and will be going for his first victory on the Saudi-funded league. He has three wins on the Korn Ferry Tour and one win on the PGA Tour Latinoamerica in 2016. Pereira is best known for making double bogey on the final hole of the PGA Championship last year at Southern Hills to miss out on a playoff by 1 shot.
Brooks Koepka, coming off a PGA Championship victory at Oak Hill for his fifth major title, shot a 69 but remained 6 shots behind with one round to play.
Phil Mickelson shot 75 and was in 43rd place in the 48-man field.
Pereira helped stake his Torque team to a three-shot lead.