Hsieh is unusual in playing with two-hands on both sides.
Simona Halep and Alexander Zverev were among top players to crash-out of Wimbledon at the All England Club today in the third round.
After an opening set which began with five straight breaks, Halep was the first to settle on serve as she held in the sixth game - but was pegged back to deuce from 40-0 up before doing so.
Instead of rushing her second serve, Hseih stepped away from the line, looked into the stands and motioned to the crowd like a cheerleader before a big fourth down, begging the fans to lend her their energy.
It will be Hsieh's first appearance in the last 16 of a Slam where she will face Dominika Cibulkova of Slovakia for a place in the quarter-finals.
"I don't learn how to be giant-killer", Hsieh said. "She (Halep) played fantastic, I had to run and fight for every point". The match was very unprofessional for me.
The Taiwanese was right about one thing, Halep did indeed fight hard.
Halep's exit means Karolina Pliskova is the last remaining top 10 seed in the tournament. And just like that the ever-unpredictable women's draw has been thrown open again.
Halep was leading 5-2 in the final set and had a match point, only to crumble to a 3-6 6-4 7-5 loss on Court One. Serena Williams is also lurking, but the American and Pliskova are both in the other half of the draw.
His win on Saturday was his third successive five-setter having also played three matches in qualifying.
This was the fourth victory against a Top 10 player for Hsieh, 32, although the former women's doubles world number 1 had never before defeated a current singles world number 1. Before her, Wozniacki's star faded after she won the Australian Open crown in January.
The world No 1 was unable to avoid the same fate as her fellow pre-tournament favourites, including defending champion Garbine Muguruza and second seed Caroline Wozniacki.
Hsieh saved a match point in the decider before prevailing 7-5 to reach the last-16 of the singles for the first time.
In this case, though, Gulbis already has been a major semifinalist - he made it that far at the 2014 French Open, but his ranking slid because of a series of injuries - while the up-and-coming, 21-year-old Zverev has yet to have that sort of breakthrough.
The way Halep was made to earn her maiden Slam though raised hopes of a more tempered run from her.
Throughout her shocking third-round upset of world No. 1 Simona Halep, Hsieh employed an endless carousel of did-you-just-see-that?! moves and, in the end, out-Haleped one of the most aggressive baseline defenders in the game.
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