The Spaniard broke his French rival three times in the first set and once in the second as he raced through in 1hr 12min at the Qi Zhong Tennis Center.
Bautista Agut's third win in a row over Tsonga pitches him into a semi-final against either defending champion Novak Djokovic or Germany's Mischa Zverev.
The 28-year-old world number 16 is now into the last four at a Masters tournament for the second time after his run to the Madrid semis in 2014.