Wawrinka became only the fourth Swiss player to reach the milestone after Roger Federer (923), Marc Rosset (433) and Jakob Hlasek (432).
"I didn't know about it before coming here," Wawrinka said. "It's been a long time on the tour and it's amazing. For sure it's special. But I was focused on the match and knew that even if I did not get here I had a chance next week."
The top-seeded Wawrinka needed little more than an hour to beat Bedene, who had ousted the Swiss player in the quarterfinals here last year in their only previous meeting on the tour.
Wawrinka started with a break and ran up a quick 5-0 lead in the first set. The 95th-ranked Bedene did manage a break in the sixth game but couldn't put up much of a fight the rest of the way.
"I'm very happy with the start this year, I feel very good," Wawrinka said. "Usually, I need a few tournaments but this time I feel good already."
Wawrinka will next play fifth-seeded Vasek Pospisil of Canada, who beat local favorite Yuki Bhambria 6-3, 6-3.
In the other quarterfinals, seventh-seeded Frenchman Edouard Roger-Vasselin saved eight break points to beat Dudi Sela of Israel 7-5, 6-7 (6), 6-0, while sixth-seeded Marcel Granollers of Spain ousted No. 4 Benoit Paire of France 6-2, 3-6, 7-6 (5).