The unseeded Czech broke Paire's serve five times, and saved both break points he faced against the eighth-seeded Frenchman. Berdych, who won the indoor hardcourt title in 2012, next faces Filip Krajinovic of Serbia in their first meeting on the ATP Tour.
No. 6 Jeremy Chardy and unseeded wild-card entry Jo-Wilfried Tsonga also won their second-round matches, setting up an all-French quarterfinal.
Chardy had nine aces in a 6-3, 7-5 win against inexperienced countryman Antoine Hoang, who came through the qualifying rounds.
Tsonga had 11 as he won 6-2, 7-6 (3) against fourth-seeded Gilles Simon, beating him for the ninth time in their 12 meetings.
The 33-year-old Tsonga's ranking has plummeted to 210 following surgery on his left knee in April.
He lost to eventual champion Novak Djokovic in the second round of the Australian Open last month.
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