Captain, Gavin Hamilton, led the Bierley innings with a patient 54, which included two fours and two sixes, although all the top order made useful contributions.
Andy Rennison (37), Lee Goddard (28), Gharib Razak (37) and Greg Wood (23) chipped in as Bierley made 255-8, despite 3-58 from Jamie Abbott.
Kez Ahmed bowled a terrific six over spell in reply, claiming 4-11, while Mitch Claydon finished with 3-36 as Baildon were all out for 155.
Bierley's reward is a home quarter-final against first division strugglers Saltaire on Sunday July 13 (start 1pm).
Woodlands survived a scare as they kept their treble hopes alive with a five-wicket win over Bradford and Bingley.
Division One leaders Woodlands were reduced to 24-5 in reply to Bingley's 127 all out, as veteran Richard McCarthy ripped through their top order with 4-6 from 10 overs, seven of which were maidens.
Nicky Rushworth (49no) and captain Tim Orrell (38no) produced an unbroken 105-run stand for the sixth wicket as they recovered to reach 129-5 from 43.4 overs.
They will entertain Manningham Mills in the quarter-finals and are also through to the quarter-finals of the Black Sheep Yorkshire Champions Trophy and travel to Central Yorkshire champions Townville on July 20.
Cleckheaton will travel to Farsley in the last eight of the Priestley Cup, while the other tie sees Esholt hosting Pudsey Congs.
Three local sides are through to the last eight of the Priestley Shield following last Sunday's second round.
Cleckheaton overcame Farsley by 32 runs and will travel to Undercliffe in the quarter-finals.
Ian Gatenby (55) and Chris Blackburn (54no) produced a 78-run partnership for the seventh wicket as Cleckheaton recovered from 93-6 to post 232-9.
H Ryatt smashed 75 in reply but Farsley fell short at 200 all out as Shaun Howe claimed 4-28.
Holders, East Bierley, defeated Woodlands by 62 runs in a repeat of last season's Shield final and they have been paired away to Morley in the last eight.
Arron Brook hit two sixes and six fours in a top score of 57, while James Petty chipped in with 33 as first division leaders Bierley were bowled out for 158, with Phil Walker claiming 3-24.
Chris Brook (3-18) and Matthew Anderson (3-14) impressed in reply as they dismissed Woodlands for 96, despite opener Tom Smallwood hitting 31.
Second division Gomersal produced the performance of the day, dumping first division title contenders Esholt out to set up a home quarter-final against Manningham Mills.
Zahir Hussain smashed 13 fours and a six on his way to 90, Craig Lightowler smashed a 33-ball half-century on his way to 62, while Matt Wilby (35) also shone in Gomersal's impressive 229-5.
Opener Tony Brassington hit 53 in reply but Paul Huddlestone claimed 5-56 as Esholt were dismissed for 145.
The final Shield quarter-final tie sees Hanging Heaton at home to Keighley on July 13.