Yastremska kept calm during the delay, reading what she called “secret” notes.
“I didn’t want to lose focus,” said the world number 24, who has won three titles over the past two seasons.
Men’s second seed Felix Auger-Aliassime converted on the first of six match points, firing a service winner to complete a 6-3, 7-6 (7/0) defeat of Australian James Duckworth.
‘Had his chances’
The 19-year-old Canadian set up a quarter-final against a second straight Aussie wild card, local Alex Bolt, who defeated German seventh seed Jan-Lennard Struff 6-3, 6-4.
“He pushed me to bring good shots when I needed them,” Auger-Aliassime said of Duckworth.
“He had chances in the second set, but I got myself to the tiebreaker — from there I played fantastic tennis.”
Women’s top seed Ashleigh Barty got a Thursday opponent as Marketa Vondrousova hammered Australia’s Arina Rodionova 6-0, 6-0 in 52 minutes.
Second seed Simona Halep will take on Aryna Sabalenka after the Belarussian booked her spot 7-6 (7/4), 6-2 over US qualifier Bernarda Pera.
Swiss wild card Belinda Bencic, the fourth seed, struggled with frustration but emerged a 7-6 (8/6), 7-6 (7/4) winner over Julia Goerges and next plays Danielle Collins, who put out seventh seed Sofia Kenin 6-3, 6-1.
Croat Donna Vekic rallied past Maria Sakkari of Greece 2-6, 7-5, 6-1, winning in two hours and overcoming six aces to reach a quarter-final against Yastremska.
In men’s play, Russian Andrey Rublev, who the Qatar Open at the weekend, beat American Sam Querrey 6-3, 6-3 to move into a last-eight clash against Britain’s Dan Evans.
Rublev, who missed six weeks in 2019 with a wrist injury, improved to a perfect 5-0 for the season.
“It’s important that I have mental confidence,” he said. “One day you still can play so good, the other day can be not that good.
Rublev’s win in Doha moved him up to number 18 in the world.
“It’s an amazing feeling to be top 20 for the first time, but there are still so many things that I can improve,” he said.
Fourth seed Pablo Carreno Busta started with a 6-3, 6-2 defeat of Frenchman Jeremy Chardy.
South African qualifier Lloyd Harris also advanced to the quarters with a 7-6 (7/5), 6-3 win over Laslo Djere 7-6 (7/5), 6-3.