The game's greatest legend did that with an 11-4, 14-12, 11-2 success against the unseeded Sarah Kippax in single figure outdoor temperatures which were almost 20 degrees celsius colder than first round matches played indoors.
David saved a game point in the second game as Kippax, who on Tuesday upset the former finalist Natalie Grinham, started to hit a better line and length, and then grew a little in confidence, advancing to 11-10.
But David responded by simplifying her game, using her consistency and mobility, before once more attempting some more ambitious attacking ploys as she stretched her lead in the third game.
"It was like day and night," she said, when asked how different the conditions for the first and second rounds had been.
"It was so bouncy on the other court (at the Pontefract squash club) and here this was so much colder and you have to work so much harder on the ball. Both of us were putting so much into hitting every shot."
David was asked how she had almost allowed Kippax to level at one game all, after which the match may have taken a different character.
"With home crowd advantage she was feeding off the crowd and going with the momentum," the champion replied. "I was just trying to make sure I took that game."
David will now have a day's rest before taking on Joelle King, the sixth-seeded New Zealander, who progressed with an 11-5, 11-7, 11-5 win over Annie Au, the 13th seed from Hong Kong.
Kasey Brown, the 12th-seeded Australian, made a tenacious recovery from two games down to beat Sarah-Jane Perry, the English surprise packet who had already despatched the seventh seeded Low Wee Wern.
"I lost last year when I was two games up, so I thought I really ought to turn this one around," said Brown after a 8-11, 9-11, 12-10, 11-7, 12-10 win in which she was twice within two points of defeat. "After the third game I thought I would win."
Brown will now face Alison Waters, the fourth-seeded English player, who lost a two-game lead but still scrambled home 11-2, 11-4, 8-11, 7-11, 11-4 against 36-year-old Rachael Grinham.
Nick Matthew, the only Englishman to have won the British Open three times, reached the quarter-finals with a 11-7, 11-3, 11-4 win over Laurens Jan Anjema, the world number 17 from The Netherlands.
Matthew, 32, next plays Karim Darwish, the former world number one from Egypt, who played with commendable accuracy in winning 11-9, 11-5, 11-6 against Daryl Selby, the world number 13 from England.
"I was pleased with the way I played, and I have always said I want to win the British Open before I retire," the 31-year-old said.
"So that's what I shall be trying to do."
Matthew is seeded to contest Sunday's final with Ramy Ashour, the man who last year took away his world title and world number one ranking, and popular opinion suggests that the Egyptian will perform another steal.
Ashour makes his bid to reach the quarter-finals on Thursday when he plays England's Chris Simpson.
Tarek Momen underlined Egypt's impressive dominance of the sport by causing the tournament's biggest upset so far - a four-game win over Peter Barker, twice a former semi-finalist.
The 25-year-old from Cairo is only his country's sixth best player, yet took advantage of the cold conditions superbly to score a 9-11, 11-4, 11-6, 11-9 win over one of the tour's most consistent top ten players. - AFP