World No 35 Verdasco had two chances to break the American's serve in the opening set but Roddick won the tiebreak 7-3 and then eased to victory.
The third seed will play 16th seed David Ferrer of Spain or unseeded Czech Radek Stepanek, a 7-6, 7-5 winner over American Mardy Fish.
Seventh seed Tommy Robredo of Spain was the highest-ranked casualty of the day, going down 6-4, 6-1 to unseeded Finn Jarkko Nieminen.
In first-round matches, twelfth seed Tommy Haas, British 14th seed Andy Murray, and Guillermo Canas, the Argentine 15th seed, all lost.
German Haas was beaten 3-6, 7-6, 6-3 by Croat Mario Ancic, having been two points from victory in the second set, while Canas was ousted 6-2, 6-2 by fellow Argentine Juan Martin Del Potro.
Murray, in only his second tournament back after a 12-week absence because of a right wrist injury, was beaten 6-1, 6-2 by Cypriot Marcos Baghdatis in just 48 minutes.
Former world No 1 Lleyton Hewitt battled past Stanislas Wawrinka of Switzerland 7-5, 3-6, 7-6 in a near three-hour marathon.
The Australian let slip a 3-0 lead in the deciding set and had to save four break points in the seventh game before squeezing through to a clash with eighth seed Richard Gasquet.
French qualifier Julien Benneteau set up a clash with top seed Roger Federer by beating Russian Dmitry Tursunov 6-4, 3-6, 6-3.
Spaniard Juan Carlos Ferrero, the runner-up last year, recovered from a break down in the final set to beat Olivier Rochus of Belgium 6-1, 3-6, 7-5.
Ninth seed James Blake beat Colombian Alejandro Falla 7-6, 6-1 to reach the second round.
Frenchman Arnaud Clement, American Robby Ginepri, Argentine Juan Monaco and Philipp Kohlschreiber of Germany also advanced to round two.
Tuesday’s results (prefix number denotes seeding):
Second round: 3-Andy Roddick (US) beat Fernando Verdasco (Spain) 7-6 (7-3), 6-2; Jarkko Nieminen (Finland) beat 7-Tommy Robredo (Spain) 6-4, 6-1
First round: Marcos Baghdatis (Cyprus) beat 14-Andy Murray (Britain) 6-1, 6-2; Radek Stepanek (Czech Republic) beat Mardy Fish (US) 7-5, 7-6 (7-3); Philipp Kohlschreiber (Germany) beat Agustin Calleri (Argentina) 7-6 (7-2), 2-6, 7-6 (9-7); Lleyton Hewitt (Australia) beat Stanislas Wawrinka (Switzerland) 7-5, 3-6, 7-6 (7-5); Arnaud Clement (France) beat Paul-Henri Mathieu (France) 6-4, 6-2; Juan Carlos Ferrero (Spain) beat Olivier Rochus (Belgium) 6-1, 3-6, 7-5; Juan Monaco
(Argentina) beat Feliciano Lopez (Spain) 6-4, 6-7 (5-7), 6-3; Julien Benneteau (France) beat Dmitry Tursunov (Russia) 6-4, 3-6, 6-3; Robby Ginepri (US) beat Jonas Bjorkman (Sweden) 6-3, 6-3.
KUZNETSOVA WINS ON RETURN
TORONTO: Third seed Svetlana Kuznetsova brushed off the rust from a month-long layoff by dispatching Italy's Roberta Vinci 6-2, 7-6 to reach the third round of the Toronto Cup on Tuesday.
Seeing her first action since a quarter-final loss to Venus Williams at Wimbledon, the Russian had looked poised for a stress-free return to the courts but was forced to dig deep to put away a stubborn Vinci.
After blasting through the first set in 29 minutes, the 2004 US Open champion needed an hour to prevail in a tense second set finally clinching the match in a tie-break 9-7.
Kuznetsova will next play the winner of American Meghann Shaughnessy and Czech Lucie Safarova for a place in the quarter-finals.
Also booking spots in the third round were Israeli 11th seed Shahar Peer with a 6-3, 6-2 win over doubles partner Tathiana Garbin of Italy and China's Shuai Peng, who advanced when 14th seed Katarina Srebotnik of Slovenia retired in the second set with a viral illness trailing 6-1, 4-2.
In opening-round action, Italian qualifier Maria Elena Camerin provided the first upset of the tournament, disposing of 15th seed Alona Bondarenko of the Ukraine 6-4, 6-3.
It was also a good day for the home crowd with three Canadians safely through to the second round for the first time 16 years.
Leading the Canuck charge was Stephanie Dubois with a shock 6-7, 6-4, 7-5 win over Japan's Ai Sugiyama.
Aleksandra Wozniak booked her spot when Russia's Anastasia Rodionova retired with a strained left quadricep down 6-4, 5-0 while Marie-Eve Pelletier and Ekaterina Shulaeva were playing in an all-Canadian nightcap.
Tuesday’s results:
Second round: 3-Svetlana Kuznetsova (Russia) beat Roberta Vinci (Italy) 6-2, 7-6 (9-7); Peng Shuai (China) beat 14-Katarina Srebotnik (Slovenia) 6-1, 4-2 – Srebotnik retired; 11-Shahar Peer (Israel) beat Tathiana Garbin (Italy) 6-3, 6-2.
First round: Marie-Eve Pelletier (Canada) beat Ekaterina Shulaeva
(Canada) 5-7, 6-4, 6-2; Aleksandra Wozniak (Canada) beat Anastasia Rodionova (Russia) 6-4, 5-0 – Rodionova retired; Maria Kirilenko (Russia) beat Martina Mueller (Germany) 6-1, 6-3; Meghann Shaughnessy (US) beat Mara Santangelo (Italy) 6-4, 7-6 (7-3); Stephanie Dubois (Canada) beat Ai Sugiyama (Japan) 6-7 (5-7), 6-4, 7-5; 13-Sybille Bammer (Austria) beat Emilie Loit (France) 6-1, 6-2; Andreja Klepac (Slovenia) beat Meilen Tu (US) 6-3, 6-1; Virginie Razzano (France) beat Aravane Rezai (France) 6-4, 4-6, 6-3; Nathalie Dechy (France) beat Emmanuelle Gagliardi (Switzerland) 6-4, 7-5; Maria Elena Camerin (Italy) beat 15-Alona Bondarenko (Ukraine) 6-4, 6-3; Eleni Daniilidou (Greece) beat Gisela Dulko (Argentina) 6-2, 6-3.—Reuters