Perry, the fifth seed who had lost her previous fourteen meetings with the three-time British Open Champion, played the game of her life to win 6-11 12-14 15-13 11-5 11-9 in 76 minutes.
"I can't believe I just beat the World No.1," said an ecstatic Perry, from Banbridge, near Belfast, afterwards. "I normally struggle to get a game off Nicol."
The win came from a stunning cross court nick shot after David served to try and save her third match-ball.
"That's definitely my best ever win," added Perry, the 32-year-old World No.8. "I've changed my game since I last played her - and did a lot of work on my movement over the summer."
But, otherwise, the day belonged to the hosts - with two English players through to the women's semi-finals for the first time since 2002.
Third seed Alison Waters and fourth seed Jenny Duncalf will provide the domestic interest in the women's semi-finals.
Duncalf went one step closer to reaching the final for the second year in a row after beating eighth seed Vanessa Atkinson, the former World Champion from the Netherlands, 11-1 10-12 11-6 11-4.
"You can never underestimate Vanessa - after all, she has been a World Champion and World No.1," said the 26-year-old World No.6. "She's got great racket skills.
"I felt I played well today and am improving all the time. This week I'll be trying to close the gap the gap behind Nicol David, the World No.1."
Duncalf will face three-time champion Rachael Grinham, the second seed from Australia who recovered from a game down to beat Lancashire's Laura Massaro 5-11 14-12 11-7 11-7.
Alison Waters claimed her first appearance in a British Open semi-final after beating Australian qualifier Donna Urquhart 6-11 11-5 11-3 11-7. The former British National champion will now meet Madeline Perry for a place in the final.
[5] Madeline Perry (IRL) bt [1] Nicol David (MAS) 6-11, 12-14, 15-13, 11-5, 11-9 (76m)
[3] Alison Waters (ENG) bt [Q] Donna Urquhart (AUS) 6-11, 11-5, 11-3, 11-7 (31m)
[4] Jenny Duncalf (ENG) bt [8] Vanessa Atkinson (NED) 11-1, 10-12, 11-6, 11-4 (39m)
[2] Rachael Grinham (AUS) bt [6] Laura Massaro (ENG) 5-11, 14-12, 11-7, 11-7 (54m)
Women's Championship Semi-Finals Line-up:
[5] Madeline Perry (IRL) v [3] Alison Waters (ENG)
[2] Rachael Grinham (AUS) v [4] Jenny Duncalf (ENG)
Issued by www.isportgroup.com/SquashNews