American Taylor Dent served and volleyed Safin off the court to win 7-5, 6-4, while world number one Federer crushed Gilles Muller 6-3, 6-2 and Hewitt beat France's Michael Llodra 6-2, 7-6.
Unable to impose his all court game, Safin grew increasingly frustrated and was warned for racket abuse in the first set.
"It was the worst match I ever played probably in my entire career," said Safin. "I haven't felt so bad on the court ever in my life.
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Dent will face 14th-seeded Argentine Guillermo Canas, a 7-5, 2-6, 6-4 winner over compatriot Juan Ignacio Chela, in the fourth round.
Federer was completely in control in his match over Muller and set up a clash with 13th seed Ivan Ljubicic of Croatia, who beat Tomas Berdych 6-4, 6-1.
The two have met three times already this year, all in finals, with Federer winning all three though the last match in Dubai was a close three-set affair.
Hewitt, who won the title in 2002 and 2003, effectively counterpunched and made fewer mistakes than Llodra.
"He's the one trying to pull the trigger all the time," said Hewitt, who will play Paul-Henri Mathieu after the Frenchman overcame Jan Hernych of the Czech Republic 6-4, 4-6, 7-6.
"He's a very flashy player. He comes up with some great winners and then he's going to make a lot of unforced errors as well. You just got to try to weather the storm."