Berdych, who must reach the semifinals to remain in contention to qualify for London for a seventh straight year, will face 10th seed Roberto Bautista Agut or Gilles Simon in the last 16.
Andy Murray is a potential quarterfinal opponent for the 2005 winner, but the Czech appeared unfazed at the prospect of also needing to beat the world No 2.
"I have to play good tennis because if you don't play your best, you don't really deserve to be there," said Berdych, who missed the US Open with appendicitis.
"Luckily, I'm healthy and can play. Who would have said that I'd be answering questions about London when I was in the hospital in Cincinnati? This is a nice bonus."
Fourth seed Milos Raonic is one of six players guaranteed their place in the eight-man field in the British capital, and the Canadian brushed aside Pablo Carreno Busta 7-6 (7/5), 6-4.
Raonic, a 2014 finalist in Paris, sent down 17 aces to take his place in the third round where the winner of 16th seed Pablo Cuevas and Paolo Lorenzi awaits him.
Richard Gasquet saved seven set points in the second set to see off Steve Johnson 6-4, 7-6 (13/11), although the 12th-seeded Frenchman is not among the seven players fighting for the two remaining London berths.
American duo Jack Sock and John Isner moved into round two following their respective straight-sets wins over Philipp Kohlschreiber and Mischa Zverev.
