“I know he’s a great player and he’s great fighting player, who is fighting for every point, every match. For me, this way that I beat him today, it’s really important,” he said.
The 32-year-old unseeded Hewitt, who had upset sixth-seeded former champion Juan Martin del Potro in the second round, gave credit to the Russian.
“In the end, he played the big games when he needed to,” the Australian said.
Earlier, women’s second seed Victoria Azarenka overcame Ana Ivanovic, the 13th seed, 4-6, 6-3, 6-4 to complete the women’s quarter-finals field after their contest was postponed from Monday due to nearly five hours of rain delays.
Azarenka, runner-up last year to Serena Williams, will play unseeded Daniela Hantuchova of Slovakia in the last eight.