Poulter is six shots back heading into the final round.
The Englishman produced an excellent sand save on the last to see him finish the day at 10 under par.
The 44-year-old’s last appearance on the PGA Tour was in mid-February.
The biennial match between the United States and Europe will now take place in September 2021 at Whistling Straits.
Organisers hope to stage the event in September 2021.
The five-time European Tour winner has yet to register a victory in the United States.
The event at Royal Troon from August 20-23 will now be the first women’s major of the year following the cancellation of the Evian Championship.
Bryson DeChambeau hopes his victory at the Rocket Mortgage Classic on Sunday has answered his critics.