MORLEY face a trip to Woodlands in the semi-finals of the Dyson Insulations Twenty 20 Cup following victories on Tuesday night.
Morley were indebted to 16-year-old George Robson, who played a key role in their thrilling three-wicket win over Baildon which took them into the semi-finals for the first time.
Robson took 5-21 as Baildon were bowled out for 108 in a match reduced to 18 overs a side.
Morley looked in trouble when Baildon openers Mubasher Khan (3-11) and Ayaz Ali (3-15) reduced them to 16-5.
Captain Matthew Baxter was determined that Morley would not capitulate and he was joined in a vital sixth-wicket stand of 60 by Richard Winn (23).
Winn was run out but Baxter held his nerve and was 47 not out when his side reached their victory target with three balls to spare.
Morley will be away to competition newcomers Woodlands in the semi-finals on either Sunday July 8 or Tuesday July 10.
Woodlands secured their semi-final spot with a 60-run win over Hartshead Moor.
Simon Mason followed up his first-round century by making 53 as his side posted 181-5. Opener Sam Frankland (33) and big-hitting Sarfraz Ahmed (30) also added quick runs.
Hartshead Moor were never in the hunt as they were dismissed for 121.
Pudsey Congs defeated Bankfoot by seven wickets to reach the semis, while the other quarter-final between East Bierley and holders Bradford & Bingley will be played next Tuesday.