James Smedley (4-36) and Joe Cooper (4-48) set up the win as Tickhill were dismissed for 148 in which Binura Fernando made 53.
Hallam remain bottom but moved closer to Aston Hall, who were bowled out for 97, a total Barnsley chased down in 20 overs.
Wickersley also eased their relegation worries, Tom Knight (46no) helping them overhaul fellow-strugglers Cleethorpes’ 104.
Things also got tighter at the top of the table where Sam Hunt (60no) and Shaaiq Choudhry (42no) took Sheffield Collegiate to an eight-wicket win over leaders Doncaster Town and reduced the gap between the two sides to 20 points.
Ben Webster starred, taking 6-20, as third-placed Wakefield Thornes crashed to 118, a total Whitley Hall passed with three wickets in hand.
Saqib Hussain (4-48) led the Elsecar attack as Treeton were dismissed for 154 before Saeed Anwar followed up a three-wicket haul with 73 to clinch the home side’s win.
There were surprises at either end of the Aire Wharfe table. Chrishna Graham (56no & 4-53) inspired Rawdon as they inflicted a first defeat of the season on leaders Otley.
Otley remain in a powerful position because second-placed Follifoot also lost at Addingham, for whom Ted Haggas hit 68 and took 5-22.
Burley made 212-9 with Chathura Kaluthanthri taking 6-67 but third-placed Horsforth fell 14 short, Nick Brook picking up 5-45.
Barry Singleton (5-35) helped dismiss Collingham for 95 to set up a victory that takes North Leeds out of the bottom two at the expense of Pool, who came up six short of Bilton’s 139.
Bottom club Methley pulled off the shock win in the Bradford Premier, skittling second-placed Bradford & Bingley for 87 in reply to 242-9, which included a century stand between Adam Patel (68) and Grant Soames (55).
Leaders Woodlands took advantage, stretching their lead with a comfortable victory at Hanging Heaton, with Muhammad Bilal hitting a rapid half-century.
Wrenthorpe’s Matthew Race included five sixes in an unbeaten 88 before Jordan Sleightholme followed up his 63 with a 4-33 spell to clinch victory over Farsley and lift his side out of the bottom two.
Harry Cullingford (63) top-scored in Pudsey St Lawrence’s 183 and there was no way back for Undercliffe after they were 8-3 after seven balls. Josh Dracup (5-47) and Richie Lamb (4-42) dismissed them for 131.
Jack Hughes picked up 4-29 as New Farnley crashed to 97 in reply to Townville’s 187 which included 60 from Jonathan Booth.
Half-centuries from Alex Stead and Christian Silkstone helped Lightcliffe to 213-9 but Cleckheaton passed that with four wickets in hand, Michael Nicholson (41) the top scorer.
Andrew Bilton (51) and a century stand between Simon Tennant (92) and Chris Bilton (67) set the platform for Yorkshire North leaders Woodhouse Grange to beat Beverley by 80 runs.
Dulash Udayanga (44) top-scored as Sheriff Hutton Bridge batted in depth to comfortably beat Yorkshire Academy.
Kyle Waite (59no) and Zac Keune (82no) saw Stamford Bridge past Dunnington’s 155 in which James Keast took 5-56.
Sam Grant took 4-31 as Scarborough fell for 92 and was 23 not out as he and Matthew Montgomery (42no) clinched victory for Clifton Alliance.
James Billington (112) and Chris Booth (59) put on 160 and with Ben Robinson making 56 not out, York set a target of 280-6 before Tom Fosdike (7-28) saw Sessay bowled out for 149.
Adbi-Hasan Ahmed (5-36) helped restrict Castleford to 135 but Harrogate could only manage 128 in reply.
Waqas Maqsood took 6-41 to set up a nine-wicket win for Hoylandswaine over Armitage Bridge. That stretched Swaine’s lead at the top of Huddersfield Premiership because Almondbury Wesleyans’ 207-7 proved too good for second-placed Scholes despite a spirited 90 from Bradley Birkhead.
Sami Aslam followed up his 6-25 with an unbeaten 73 to inspire bottom club Shelley to victory at Barkisland.