Dimitrov, the Bulgarian seventh seed, looked out of sorts early before claiming a 0-6 6-3 6-4 6-1 win over in-form Belgian David Goffin.
Goffin, who went on a 25-match winning run after Wimbledon, looked as confident as Dimitrov did shaky during a 26-minute first set.
But Dimitrov's ability to take his chances during the second and third sets proved to be decisive.
The 23-year-old will need to be in better form in the fourth round, when he faces Frenchman Gael Monfils.
Monfils, the 20th seed, looked in ominous form in a 6-4 6-2 6-2 thrashing of countryman and 12th seed Richard Gasquet.
The exciting and unpredictable Monfils hit 50 winners in his victory.
Czech Berdych was never likely to be troubled by Russian Teymuraz Gabashvili, and that proved to be the case as the sixth seed won 6-3 6-2 6-4.
It was a quick finish Berdych needed, having being pushed to five sets by Martin Klizan in the second round.
He is likely to face a bigger test in the fourth round as a meeting with Austrian Dominic Thiem awaits.
The talented 20-year-old was too good for Spanish 19th seed Feliciano Lopez 6-4 6-2 6-3.
Swiss second seed and 17-time grand slam champion Roger Federer battled early in his 4-6 6-1 6-1 6-1 win over Spain's Marcel Granollers.
Federer won 20 of the final 24 games after a two-hour rain delay.
A potentially tricky fourth-round clash awaits against 17th seed Roberto Bautista Agut after the Spaniard eased past Frenchman Adrian Mannarino 7-5 6-2 6-3.
Spanish fourth seed David Ferrer was beaten 6-3 3-6 6-1 6-3 by French 26th seed Gilles Simon.
Simon will face Marin Cilic after the Croatian 14th seed's 6-3 3-6 6-3 6-4 win over South African 18th seed Kevin Anderson.