Swiss beat Andy Roddick, while Serbian got past Jo-Wilfried Tsonga in quarter-finals
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Federer, who won back-to-back titles here in 2005 and 2006, closed out the match with a service break, earning a match point with a backhand winner that clipped the net cord and found the corner.
Another backhand found Roddick helpess at the net.
"It's easier if I would have just played terrible the whole time," said Roddick, who thrilled the crowd of 14,000 by taking the second set.
But in the hard-fought third, Roddick failed to convert two game points in the final game.
"I at least gave it a go there in the third, and didn't really catch a break there," he said.
Djokovic, who had lost his last four encounters with Tsonga, reversed that trend despite receiving treatment for apparent heat-related symptoms in the second set.
Djokovic broke Tsonga to take a 4-2 lead in the second, saved two break points in the eighth game and was under pressure again as he served for the match at 5-4 but closed out the victory in just under two hours.
Djokovic, who said he had been battling a stomach ailment on Tuesday, said that the after-effects, the heat and the pressure of the match combined to affect him.
But he still displayed precise, powerful groundstrokes that had Tsonga on the defensive from the start.
"I have to be very happy with today's performance, because I have been struggling to find a way to win against him in the last four encounters," he said. "I just knew that I needed to stick in and try to wait for my chances and be aggressive.
"Today I think I tried to be closer to the line, more in control, and just put the pressure on him. So I think that's what I did."
The other men's quarter-finals on Thursday pit world number one Rafael Nadal against sixth-seeded Argentinian Juan Martin del Potro and fourth-seede Briton Andy Murray against Spain's eighth seed Fernando Verdasco.
Nadal, the Australian Open champion, is gunning for his second straight prestigious Masters 1000 title in as many starts after his triumph in Indian Wells, California.
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