Berdych, a semi-finalist at Flushing Meadows in 2012, overcame Slovakian left-hander Martin Klizan 6-3 4-6 6-2 3-6 6-3 in three hours 45 minutes.
It was more difficult than expected for Berdych, who has a kind draw awaiting him in New York.
The Czech sixth seed will face Teymuraz Gabashvili after the Russian beat countryman Alexander Kudryavtsev 6-1 6-4 7-6 (7-4).
Dimitrov, another outsider for his maiden grand slam title, was far more convincing.
The Bulgarian seventh seed and Wimbledon semi-finalist thrashed Israeli Dudi Sela 6-1 6-2 6-2.
Dimitrov was on court for just one hour 29 minutes, hitting 28 winners to set up a meeting with David Goffin.
The in-form Belgian also cruised, crushing Portuguese 32nd seed Joao Sousa 6-4 6-2 6-0.
Swiss 17-time grand slam champion Roger Federer remains on track after cruising past big-serving Australian Sam Groth 6-4 6-4 6-4 under lights on Arthur Ashe Stadium.
Another Spaniard, Marcel Granollers, fought his way past towering Croatian 25th seed Ivo Karlovic 7-6 (8-6) 6-7 (3-7) 7-6 (7-5) 3-6 6-4 to set up a clash against Federer.
Spaniard David Ferrer had the easiest of passages through after Australian Bernard Tomic handed him a walkover due to a hip injury.
Setting up a clash against Ferrer was French 26th seed Gilles Simon, who claimed a 6-4 3-6 7-5 6-1 win over Argentine Federico Delbonis.
French 20th seed Gael Monfils was relatively comfortable in a 7-5 6-3 6-2 win over Colombian Alejandro Gonzalez.
An all-French affair follows in the third round, with Monfils to face Richard Gasquet after the 12th seed beat Italian journeyman Paolo Lorenzi 7-6 (7-4) 6-3 6-3.
Pole Jerzy Janowicz suffered a 6-7 (6-8) 6-2 6-1 6-3 loss to South African 18th seed Kevin Anderson, who next meets Marin Cilic.
Croatian 14th seed Cilic was too good for Ukrainian Illya Marchenko in a 7-6 (7-2) 6-2 6-4 victory.
Roberto Bautista Agut, the Spanish 17th seed, beat American Tim Smyczek 6-3 6-2 6-1 to set up a meeting with Frenchman Adrian Mannarino, who upset Italian 15th seed Fabio Fognini 6-3 6-4 6-1.
Another Spaniard, Feliciano Lopez, and Austrian Dominic Thiem also progressed.
Lopez, the 19th seed, overcame Japan's Tatsuma Ito 6-4 3-6 6-4 7-6 (7-4) and Thiem upset Latvian 11th seed Ernests Gulbis 4-6 3-6 6-4 6-3 6-3.