20-time Grand Slam winner, Federer, routed Britain's 58th-ranked Dan Evans 6-2, 6-2, 6-1 in only 80 minutes.
He blasted 48 winners to just seven for Evans.
"I really enjoyed myself," Federer said. "I was able to adjust and take care of business so it was good."
Federer will play Belgian and 15th seed David Goffin in the next round.
Djoker counts on massive improvement
Djokovic was unfazed by a left shoulder pain to beat 111th-ranked American Denis Kudla 6-3, 6-4, 6-2.
He set up a date with Stan Wawrinka, the Swiss 23rd seed who overcame Paolo Lorenzi 6-4, 7-6 (11/9), 7-6 (7/4).
"That I managed to play almost pain-free, that's a big improvement from last match obviously," Djokovic said.
Nishikori ousted, Medvedev wins
Japanese seventh seed Nishikori was stunned by 20-year-old Aussie De Minaur 6-2, 6-4, 2-6, 6-3. De Minaur will face Bulgaria's Grigor Dimitrov next. Russian fifth seed Daniil Medvedev progressed to the last 16 with a 7-6 (7/1), 6-4, 7-6 (9/7), 6-4 victory over Feliciano Lopez.