Mayer, seeded 15th, dumped Fabio Fognini 6-0, 6-2, losing only six points in his seven service games. He also won 61 percent of the points off Fognini's serve.
Mayer dropped a mere five points in sweeping through the first set and won 17-of-20 points on serve in the second.
The other main-draw match Sunday saw 13th-seeded Stanislas Wawrinka defeat Juan Monaco 3-6, 6-3, 6-3. Wawrinka recorded a pair of breaks in each the second and third sets in advancing.
With world Mo. 1 Novak Djokovic missing the tournament because of a back injury and No. 3-ranked Roger Federer also skipping the event, the top seeds in Shanghai are world No. 2 Rafael Nadal and fourth-ranked Andy Murray.
Murray, the Shanghai defending champion, beat Nadal Sunday in a three-set title match at the Rakuten Japan Open Tennis Championships in Tokyo.
Notable deaths of 2014 [PHOTOS]