In only his third career meeting with a top-10 player Purcell stunned an opponent who has reached three of the last six grand slam finals.
His 6-4 3-6 6-4 victory came in just under two hours with Purcell hitting 38 winners and impressing at the net.
Purcell was outside the world's top 200 a year ago, and seen primarily as a doubles player, but rocketed up the singles rankings early this year with an impressive spell on the Asian circuit.
Despite disappointing results in the European claycourt swing, and on grass, when he was hampered by an ankle injury, Purcell has stayed in the top 80 since May and is now seeking to push on in the north American hardcourt season.
Norwegian fifth-seed Ruud is ranked 63 places above Purcell, but encountered stiff resistance in the pair's first meeting on the tour since Ruud won 7-6 (7-5) 7-5 in US Open qualifying five years ago.
Under a blue Ohio sky, on the blue hardcourt, the Sydneysider took the first set 6-4 but was pegged back in the second 3-6.
In the third set Purcell forced a break point at 4-3 but Ruud's serve set up a smash he could not return. The 25-year-old then faced three break points of his own in the next game, but fended them off.
Having then held his serve to be 5-4 up, two long forehands from Ruud then presented Purcell with successively a match point, and victory.
In the last 16 Purcell will face either world No.10 Frances Tiafoe or former grand slam champ Stan Wawrinka.
Australian No.1 Alex de Minaur was due on court 4 after Purcell, to face French veteran Gael Monfils. The winner will meet the victor in the night session headline match between Novak Djokovic and Spain's Alejandro Davidovich Fokina.
Already in the third round is Alexei Popyrin, after winning his second round tie on a walkover after opponent Nicolas Jarry withdrew to return to Chile for the birth of his second child.
Earlier former champion Daniil Medvedev beat Italy's Lorenzo Musetti 6-3 6-2.
Medvedev, who also beat Musetti at last week's Canadian Open before losing in the quarter-finals, broke the Italian twice in each set en route to sealing victory in 77 minutes.
"We both made some mistakes, we both made some double faults and stuff like this," third seed Medvedev, who served five double faults, said.
"But I managed to be a little bit better in the important moments."
There were home victories for Tommy Paul and Taylor Fritz, who defeated Ugo Humbert and Lorenzo Sonego respectively.
Alexander Zverev also progressed, beating Yoshihito Nishioka 7-5 6-4.
7°C