Haas took control of the match late on Oakmont Country Club's back nine after a birdie at the 14th gave him a 1-up advantage. Haas, a 2002 semifinalist, extended his lead with a par at the 16th and closed out the match with a par at the 17th after Persons made bogey.
Haas will square off against Zach Atkinson in Thursday afternoon's third round. Atkinson defeated Steve Slayden in the second round.
David Oh never trailed in his match with Trip Kuehne and coasted to a 3-and-1 victory to advance to the third round of match play. Oh will meet Matt Kohn in the third round.
George Zahringer defeated Korey Mahoney, 4 and 2, while Michael McDermott ousted medalist John Holmes, 1-up. McDermott will face Patrick Carter in the third round.
'I compete against college kids all the time. They all look the same to me,' said the 50-year-old Zahringer. 'With the driver, I can't keep up with them, but my iron game is on the level.'
Gregg Jones routed Tom Glissmeyer, 7 and 5, to advance.
The third round of match play is scheduled for Thursday afternoon.
The U.S. Amateur is one of 13 national championships conducted annually by the United States Golf Association, with 10 of the events strictly for amateurs.