The 2005 Paris champion won five straight games in the first set to rally from a 3-1 deficit, hitting 12 winners to only three for Verdasco.
Berdych then broke the Spaniard twice for a 5-2 lead in the second set but wasted four match points to let Verdasco level at 5-5.
Yet, the fifth-seeded Czech broke Verdasco again with a forehand pass before clinching victory with a crosscourt backhand winner.
Andy Roddick also moved into the third round by downing Julien Benneteau of France 6-4, 6-4.
The 13th-seeded American made only 12 unforced errors compared to 25 for Benneteau.
Roddick hit a forehand return winner followed by a running forehand winner down the line to take the first set.
The 2003 US Open champion rallied from 3-1 down in the final set to convert his first match point with a backhand volley.
Meanwhile, Feliciano Lopez of Spain, Ivan Dodig of Croatia, Sergiy Stakhovsky of Ukraine and Jeremy Chardy of France won their first-round matches.
Lopez beat Michael Llodra of France 7-6 (7), 6-3, Dodig rallied past Fabio Fognini of Italy 4-6, 6-1, 6-3, and Stakhovsky defeated Kei Nishikori of Japan 6-4, 6-3.
Dodig will next take on top-seeded Novak Djokovic.
Lopez saved four set points in the tiebreaker before jumping to a 4-0 lead in the second set and firing an ace to clinch victory.
The Spanish lefty will next play eighth-seeded Gael Monfils of France.
Nishikori got a cold dose of reality after stunning Djokovic last weekend to reach the final of the Swiss Indoors in Basel. He could only convert two of 14 break chances against Stakhovsky, who won to meet Viktor Troicki of Serbia.
Marcel Granollers of Spain had not recovered from his heroics of last weekend either as the Valencia Open winner lost the first set 6-3 to Chardy before retiring because of an ankle injury.
Chardy broke Granollers at 3-2 and clinched victory by cracking three aces in the final game. The Frenchman moved on to face second-seeded Andy Murray.
