Centuries by Connor Williams and Vikram Rathour helped Birstall to a third win of the season and they are now six points off leaders Wrenthorpe.
Rathour fired 103 and opener Williams 105 not out, supported by Rob McFarlane (32) as Birstall reached 260-2.
Captain John Carruthers then led the way with 4-25 as Thornes were reduced to 90-6. Phil Callaghan (46) and Scott Wightman (30no) offered resistance but Richard Pearson's 3-53 haul, added to Paul Blakeley's 2-35 earlier, saw Thornes 195 all out.
Batley suffered an eight-wicket reverse by Methley at Mount Pleasant. Mohammed Tahir made 33 and Kashif Talib 27 in Batley's modest 125-8 as Chris Kippax claimed 4-27.
Tariq Hussain and Mohammed Ishtiaq then took a wicket each but Methley cruised to 129-2 in 45 overs, led by John Proud (64).
Birstall A slipped to second in Division Two after losing by 51 runs to Wakefield City A.
Dave Hilton (4-50) and Malcolm Ellis (3-33) helped dismiss City for 233 as A Amjad hit 52.
In reply Rob Ellis (39), Adam Holroyd (33) and Mark Heseldin (30) made useful runs but 6-31 by Amjad saw Birstall out for 182.
Woodkirk restricted hosts East Ardsley A to 148-9 but in the end Ardsley ran out 59-run victors.
Woodkirk's bowlers were led by Patrick Hinchcliffe (3-14 in 13 overs) and Garry Dawber (3-36).
Opener Stephen Dawber (35) tried to anchor the innings but only Hinchcliffe (22no) made double figures as Woodkirk were 89 all out, with Michael Pearson taking 5-23.
Soyeb Rayat (23) and Ramran Rashid (28) saw Batley A all out for 126 at Wakefield St Michael's A as Brian Stephens took 5-16.
The hosts appeared in control at 103-4 but Batley fought back with five wickets for 12 runs. Waseem Rabani took 3-31 and Yusaf Kayat 3-24 but the Saints staggered home at 127-9.
Woodkirk A suffered a six-wicket defeat by visitors Hunslet Nelson A in Division Four.