Edmund, 25, defeated Canadian fourth seed Felix Auger-Aliassime 6-4 6-4 to set up a meeting with American Taylor Fritz.

Watson, 27, overcame Ukraine's Kateryna Bondarenko 7-6 (7-2) 6-2.

Meanwhile, Boulter fell to a 7-6 (7-2) 7-5 defeat by sixth seed Zhu.

After losing a disappointing first-set tie-break, 23-year-old Boulter responded well as she cemented an early break of serve in the second to establish a 3-1 lead.

But Zhu fought back to grab her second break point opportunity and draw level at 4-4 before seeing out the match with another break.

British number two Watson, ranked 69 in the world, saved two set points at 5-4 down before dominating a tie-break at the end of a topsy-turvy opening set where each player held serve just twice.

Watson made significantly fewer mistakes in the second set, racing into a 3-0 lead and eventually sealing victory with her first match point on Bondarenko's serve.

She will now face the American Christina McHale for a place in the semi-finals.

Watson said: "Christina is a good friend of mine. We're the same age, we came through juniors together and we've been on the same journey since we were very young."

British men's number two Edmund produced an impressive display to beat talented 19-year-old Auger-Aliassime.

Edmund, ranked 44th in the world, broke the Canadian world number 19's serve early in both sets and held on to his advantage relatively untroubled to continue his recent run of form.

Elsewhere, world number two Rafael Nadal remains on course for a third Mexico Open title after defeating Serb Miomir Kecmanovic 6-2 7-5. He will now play South Korea's Kwon Soon-woo in the last eight.

If Nadal wins the Acapulco title and Novak Djokovic loses his semi-final match at this week's Dubai Tennis Championships the Spaniard will regain top spot in the rankings.