The 33-year-old Hsieh ultimately scorched into the last eight, converting three break points to bagel her German opponent.
Hsieh, who recorded her first win in three attempts against Kerber, will next face Karolina Pliskova for a place in her second semi-final of the season, and first since the opening week of 2019 at the Auckland Classic.
"How did I win? I try very hard," Hsieh said after notching up her first victory over a top 10 opponent since beating Simona Halep at last year's Wimbledon.
"The first two sets, we both try super hard, so it was very close. Final set, I did little bit more. I feel more relaxed in the final set, so I gained the match pretty well."
World number four Petra Kvitova overcame American qualifier Jennifer Brady 7-5 1-6 6-3 to reach the last eight in Dubai for the first time in six years.
Australian Open runner-up Kvitova was two points away from losing the opening set in the ninth game when she responded in style by clinching 14 of the next 16 points.
After defeating Katerina Siniakova in three sets in the second round, Kvitova had said on Twitter she was "glad P3tra came back" - and the two-time Wimbledon champion was forced to step up her game again in a decider against Brady.
Kvitova benefited from Brady's sixth double fault of the match to secure a break in the first game before producing a string of delightful serve and volley combinations to extend her lead.
While Kvitova squandered her first match point by producing a 10th double fault, the Czech sealed a victory with a clinical point finished at the net.
"The wind was just terrible today, to be honest," said Kvitova after reaching at least the quarter-finals for the fourth successive tournament.
"It was really difficult to find a way with it. I couldn't really serve well today at all. It's been big struggle for me."
Third seed Simona Halep joined Kvitova in the quarter-finals after the Romanian continued her steady progress with a 6-3 7-5 win over Ukraine's Lesia Tsurenko.
Two-time defending champion Elina Svitolina extended her winning streak in Dubai to 11 matches after defeating two-times Grand Slam champion Garbine Muguruza 6-1 6-2.
(Reporting by Hardik Vyas in Bengaluru, editing by Pritha Sarkar)
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