At the Centre Court on Monday, Federer, seeded no. 3, had no time to lose as he spent just 97 minutes to get rid of Dimitrov, who saw his serve broken five times, while he managed to break his rival's serve once, Efe news reported.
The 35-year-old Federer won for the sixth time in a row over the 2017 Sofia and Brisbane champion Dimitrov, former world number 8.
The seven-time Wimbledon champion, who is eyeing his record extending 19th Grand Slam title, is set to play against Canadian Milos Raonic, seeded number 6.
The 2016 Wimbledon finalist Raonic beat German Alexander Zverev, 20, 4-6, 7-5, 4-6, 7-5, 6-1.
On the other hand, World No. 1 Andy Murray advanced to the quarterfinals at Wimbledon by defeating his French opponent Benoit Paire 7-6 (1), 6-4, 6-4.
The defending champion on Monday needed two hours and 21 minutes to secure a spot in the quarterfinals for the tenth time in a row at Wimbledon, and the 30th time in a Grand Slam, Efe news reported.
Murray, two-time Wimbledon champion, saw his serve broken twice in the first set, but he managed to win the first set through a tiebreak, to sail easily through the match to the next round.
The 30-year-old Briton, seeded and world no. 1, is now set to play against American Sam Querrey, seeded no 24, who beat South African Kevin Anderson 5-7, 7-6 (5), 6-3, 6-7 (11), 6-3.
Croatian Marin Cilic, seeded number 7, saw off Spanish Roberto Bautista Agut seeded no. 18, 6-2, 6-2, 6-2.
Cilic is now set to play the winner between Spanish Rafael Nadal and Gilles Muller of Luxembourg.