Nadal had to save six break points in the opening set before easing to a 7-5 6-1 6-4 victory over 14th seed Kevin Anderson, while Berdych saw off home hope Bernard Tomic 6-2 7-6 (7/3) 6-2.
Third seed Nadal admitted he thought of quitting during his second round match with American Tim Smyczek on Wednesday, the Spaniard suffering from dizziness and nausea as he fell two sets to one behind.
However, the nine-time French Open champion dug deep to battle back and win in five sets and looks to be working his way back to form and full fitness after the latter half of 2014 was ruined by a wrist injury and appendicitis.
The 28-year-old had to save a break point in the fifth game of the first set and five more in the 11th before finally getting a chance to break the big-hitting Anderson, who netted a simple volley to give Nadal the set.
From that point there was only going to be one winner and Berdych will have to improve his dreadful record against Nadal to reach the semi-finals in Melbourne for the second year running.
Nadal has an 18-3 record against the seventh seeded Czech, who won three of their first four meetings but has lost the last 17 in a row.
“It’s very special to be in the quarter-finals after a tough period of time for me, it’s a fantastic result,” Nadal said.