Gauff, 15, continued her stunning form from Wimbledon by qualifying for the third WTA main draw of her career.
Playing in front of a packed court in the American capital, she was beaten 6-4 6-2 against world number 84 Diyas.
It was her first main-draw appearance since SW19, where she beat Venus Williams on her way to the last 16.
Gauff, who has climbed up to 146th in the world after her recent exploits, was the youngest woman to reach the second week at the All England Club since Jennifer Capriati in 1991.
Meanwhile, top seed and former champion Sloane Stephens suffered a shock 6-2 7-5 first-round loss to Swede Rebecca Peterson on Tuesday.