The Davyhulme Park 14 handicapper knew she had a battle on her hands because her Oldham opponent had knocked out double winner Gina Brown in the previous round.
But recently-retired bank manager Cheryl, 57, cashed in on the four strokes Beverley handed her and charged to a 4&2 victory over her own course.
"I was always in front but it was one of those days when I played fairly well," she said.
And she will have to stay in the same groove tomorrow when she meets England player Rachael Goodall in the semi- finals at Swinton Park.
This season the two-rank Heswall teenager has won the Cheshire Women's and Northern Girls' championships and beat England champion Hannah Barwood in the Harper Salver at Bath.
"She will be difficult to overcome, despite giving me plenty of shots," added Cheryl whose biggest achievement to date is winning lady captain's prize at her club.
Brookdale's Victoria Akin, a three and two winner over Withington's Carolynn Sullivan, takes on West Derby's Jill Hopwood in the other semi-final. The action starts at 11.30am.
The finals are at Marriott Worsley Park next Friday (9.30am).
DENTON player Darryl Coleman has no regrets about making the long trip to Carnoustie as a stand-in for his pal Cyril Crooke - he holed in one at the 161-yard 16th at last year's Open Championship venue during the first round of the Tassie. The 34-year-old nine handicapper is among dozens of regional golfers, including several from his home club, and Lancashire captain Bill Beaumont, who annually support the week-long competition played over Carnoustie and Burnside.
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