China's Shi, ranked 217th in the world, stuck to her strategy of targeting the edges of the court despite a first-set loss to the 13th seed, and pushed Eala back with powerful serves as she stormed to victory, cheered on by the home crowd.
"I tried to push myself in the serve... tried my best to win," said the 21-year-old, who held her head in disbelief after her first win over a top-20 ranked opponent.
The Philippines' Eala, who has risen to prominence with seven wins over top-10 ranked opponents this year, has struggled with her form over the last month, having also lost to 180th-ranked Tatiana Prozorova at the Singapore Open last month.