It took the Swiss maestro only an hour to dispatch his Ukrainian opponent.
Federer is well known for how quickly he likes to play between points.
But in the first set, the 36-year-old exceeded himself by taking just 47 seconds to produce a breathtaking demonstration of his class.
Serving at 4-3, with a break, Federer stepped up to the baseline and hit an ace to down the T to lead 15-0.
The second seed then struck another ace wide to Dolgopolov’s backhand.
At 30-0, Federer sliced another first serve ace wide past an agitated Dolgopolov.
Then to put the finishing touch on the game, the 19-time Grand Slam winner made it four consecutive first serves and though Dolgopolov this time got a racket onto it, the ball flew well wide of the court.
It was Swiss efficiency to the highest degree and after the match, Federer expressed his delight after such a clinical performance.
“I felt good in the first match I played [against Diego Schwartzman] and today was exactly the same,” he said after his 60-minute win.
“I think maybe the matchup was maybe a bit easier and I took my chances more.
“Plus I had a better ratio of winning on the break points that I didn’t quite have against Schwartzman.
“That’s maybe the biggest difference of both matches, so I’m happy I was able to do better today on the break points.”
Federer faces Frenchman Richard Gasquet for a place in the semi-finals later today.