Bridge made a solid start with openers Pradeeptha Gunaratne (42) and Ryan Gibson (65) sharing a century stand.
Ryan McKendry weighed in with 62 but when they were dismissed for 195, York looked favourites. However, despite a half-century from Nick James, they still came up just short.
Second-placed Woodhouse Grange fared even worse at Harrogate who, with George Ross (62) and William Bates (46no) leading the way, set a target of 231-8. Tom Geeson-Brown (5-26) ensured Grange were always on the back foot and the 77-run win lifted Harrogate out of the bottom two.
Half-centuries from Darren Harland and Oliver Stephenson helped Scarborough to 224-8 and even though Dulash Udayanga and Robert Stevens responded in kind, Sheriff Hutton Bridge lost by 21 runs and slipped to fourth in the table below Stamford Bridge.
Alec Drury (60), Grant Halder (79) and Danny Broumpton (53no) starred as Driffield Town eased to a 122-run win over Clifton Alliance, and a 5-29 spell from Harry Sullivan helped dismiss Acomb for 108 in reply to Yorkshire Academy’s 217-8 that included a half-century from George Hill.
David Wainwright (64) was top scorer in Castleford’s 240-8 and then took 5-38 as Sessay were restricted to 209-8, despite being given a good start by Mark Wilkie (50), Matthew Till (43) and Mark Jackson (70no).
Wakefield Thornes recaptured top spot from Sheffield Collegiate in Yorkshire South after beating them in a low-scoring affair.
Mahmood Rasool (5-39) helped restrict Collegiate to 159 despite a late burst led by No 8 Henry Eldred (44). Thornes did not find batting easy but got over the line with three overs to spare.
Harpreet Singh (103) took his league tally to 778 runs with his sixth century in seven matches and he put on 130 with Eli Richards (104no) as Barnsley hit 271-4. Doncaster Town fell 25 short after Ali Waqas was run out on 94.
Ryan Schierhout (61) was the main contributor to Appleby Frodingham’s 238-8 and then took 4-51 and teamed up with Kieran Watson (4-54) to bowl out Whitley Hall for 193, in which Greig Batty was 51 not out.
Brothers James (76) and Alex Osmond (6-55) starred as Cleethorpes beat Treeton by 22 runs, while Hallam had three wickets in hand when they passed Whiston’s 132, which included 61 from Sajid Khan.
Ali Manzoor (6-26) and Mark Cummins (3-28) skittled Aston Hall for 89 before Cummins (36no) and Thomas Knight (34no) eased Wickersley to victory.
A third win in a row edged Cleckheaton away from the relegation zone in Bradford Premier. Toby Thorpe (83) and John Wood with a rapid 59, steered them to 272-8 and even though Sohail Raz followed up a five-wicket haul with a top score of 37, Methley were dismissed for 182, Nick Walker taking 5-54.
Simon Lambert hit 110 not out and Andrew Brewster and Ajmal Shahzad each took four wickets as leaders New Farnley crushed bottom club East Bierley by 179 runs.
An unbeaten 48, including five sixes, from No 9 Nathan Lumb was the highlight of Farsley’s 187-8 on the way to beating Scholes by 23 runs.
Shahid Nawaz (5-57) helped restrict Hanging Heaton to 206 and Townville looked set for victory until Ritchie Bresnan (56) and Conor Harvey (32) were parted and they fell five runs short.
Suleman Khan (115) put on 159 with Rhys Jowett (62) and then took 5-28 to clinch Lightcliffe’s 94-run win over Bradford & Bingley.
A century from Mark Robertshaw put Pudsey St Lawrence on the way to a comfortable win at Woodlands.
Alex Lees (80no) and Muhammad Anwar (58) steered Huddersfield Premiership leaders Hoylandswaine to victory over Scholes.
Second-placed Honley slipped back after Moorlands’ Nathan Rabnot (97) and Eddie Walmsley (67no) clinched a six-wicket win.
It is as you were at the top of the Aire-Wharfe with Billy Hyde (5-29) helping leaders Otley overcome third-placed Rawdon, while Nick Brook (41 and 5-11) starred as second-placed Burley beat Beckwithshaw.