Fifth seeded Norrie lost the opening set in the last 16 clash against Australia's Jordan Thompson in west London.
But Norrie recovered his composure to dispatch the world number 76 in a 4-6, 6-3, 6-2 win that secured a sixth quarter-final appearance on the ATP Tour this year.
The South Africa-born 27-year-old is hoping to emulate last year's run to the Wimbledon semi-finals when the grass-court Grand Slam gets underway on July 3.
Norrie was beaten by eventual champion Novak Djokovic in the Wimbledon last four.
Ranked 13th in the world, Norrie defeated Miomir Kecmanovic in the Queen's first round before holding his nerve to survive against Thompson.
"I think it was the perfect match. Jordan really likes the grass and in the first set he played a couple of good points to beat me," Norrie said.
"I came out with a lot of energy in the third set and that's what got me through.
"It's really good to be that consistent but you always want more as a tennis player. I want to keep pushing for more, especially in the bigger tournaments."
Norrie was also due to play doubles with Andy Murray on Wednesday but the two-time Wimbledon champion, who lost in the singles on Tuesday, withdrew through fatigue.
In Friday's quarter-finals, Norrie, the Queen's runner-up in 2021, faces Sebastian Korda, who defeated fellow American Frances Tiafoe 7-6 (7-2), 6-3.
Norrie's compatriot Ryan Peniston was unable to replicate last year's debut run to the Queen's quarter-finals.
Peniston is ranked 259 places below Holger Rune and the Danish world number six eased to a 6-3, 6-4 victory as he chases the title on his Queen's debut.
