The Czech seemed to be cruising after taking the first two sets before his German opponent hit back in the third.
However, Berdych regained his composure to race to victory in the fourth set, with a 6-3 6-4 4-6 6-1 win.
He will now face the winner of Jiri Vesely and Jaoa Sousa.
Australian Open
Australian Open order of play, Day 2 – Raducanu and Murray fly GB flag
YESTERDAY AT 15:24
More to follow.
Australian Open
'Always perfection' - Zverev hails Federer and Nadal after grinding out win
YESTERDAY AT 13:44
Australian Open
Zverev battles past stubborn Altmaier to reach second round of Australian Open
YESTERDAY AT 12:38