Rublev's win sets up an all-Russian quarter-final with ninth seed Daniil Medvedev.
"It's my biggest and the most emotional win", Rublev said after reaching his first Masters quarterfinal.
"I will go to fight, to try to win, give my best and then we'll see what happens". He was everywhere. It was tough for me, but an excellent match by him. "It's a straight-sets win but probably the score doesn't indicate how tough it was on the court".
"It is such an awesome feeling when you're playing a legend like Roger and all these people supporting him until the end", Rublev told ESPN in an on-court interview.
After defeating Dominic Thiem in the quarter-finals at Hamburg a week back, Rublev has had a phenomenal week coming through the qualifiers and defeating Nikoloz Basilashvili, Stanislas Wawrink and now Roger Federer back-to-back thereafter.
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Main rival Novak Djokovic progressed to the semi-finals.
"I just would have hoped for an overall better performance".
The 21-year-old Rublev was down in 70th in the ATP Rankings in the wake of injury woes.
"I played 45 matches this year, so I think I should be fine", said Federer. "It may not have been there the whole match, but we were able to find it when we needed it".
But a surprise two-set loss - his fastest defeat in 16 years - saw the Swiss maestro dumped out of Cincinnati and delivered a blow to his US Open preparations. I had to serve well, which I have done, and it got me out of the trouble especially in the second set when I had to face some break points. I had to really think about what I had to do during the match, so I'm not that mad at the result. "My goal is to get back playing at the level that I want to on the singles court, and I've decided that I need to focus all my energies on that right now", Murray told BBC Sport.
Belgium's David Goffin and Japan's Yoshihito Nishioka also advanced to set up a quarterfinal match-up.