The Irishman finished two strokes clear at Woburn.
Stenson was stripped of the Ryder Cup captaincy after joining the Saudi-funded circuit last July.
Thomas is bidding to win his third US PGA title at a venue which last staged the event in 2013.
Spieth, who needs to win the US PGA to complete the grand slam, is suffering from an untimely wrist injury.
The South Korean Seung-yul Noh leads despite cracking his driver on the 12th hole.
Players have been fined up to £100,000 for each breach of the Tour’s regulations.
The American has struggled with his putter lately.
Woods was not included in the 155-strong field issued by the PGA for next week’s event at Oak Hill Country Club.
Popert will be among 80 male and female players from 19 countries competing at Woburn from May 10-12.
The American will be seeking to complete a career Grand Slam at Oak Hill later this month.
