Wawrinka broke Seppi three times to take the first set. He started the second with two consecutive aces and broke Seppi twice more for a comfortable victory at the Royal Tennis Hall in the Swedish capital.
"It was almost a perfect match for me," Wawrinka said.
Wawrinka will next face the winner of Swedish qualifier Filip Prpic and Robin Haase of the Netherlands.
Swedish wild card Michael Ryderstedt - ranked 392nd - also advanced after beating Daniel Gimeno-Traver of Spain 7-6 (3), 6-3. Gimeno-Traver's eight aces weren't enough to overcome an opponent ranked 331 spots below him.
Finland's Jarkko Nieminen overcame a poor start to beat Michael Berrer of Germany 4-6, 6-1, 6-4.
Top-seeded Roger Federer and Swedish favorite Robin Soderling enter the indoor hard-court tournament in the second round later this week, as do third-seeded Tomas Berdych of the Czech Republic and fourth-seeded Ivan Ljubicic of Croatia.
Soderling, Berdych ousted in Malaysian OpenNadal set for Mallorca role
