It felt uncertain when there was a tiebreak in the second set, but 59-ranked Peterson controlled it completely and won 7-1.
After the Egyptian Sheriff, ranked 118th in the world, knocked out the ball, the victory was in port and Peterson could discuss with his father and coach Mart down on the blue court in the sunshine.
Peterson looked to win the first set easily as she went 5-1.
But the Egyptian worked her way into the match, becoming 5-5, and Peterson could easily win it 7-5.
The 15th-seeded Elena Rybakina is waiting in the second round.