A stand of 74 between Georgy Drury (44no) and Luke Kilby (45) had helped Dunnington to 173-6 but Bridge got home with eight balls to spare.
Woodhouse Grange took over top spot with victory over Clifton Alliance, Andrew Bilton (54) and Tom Neal (4-30) leading the way.
David Wainwright starred with an unbeaten 116 as Castleford climbed out of the bottom two, chasing down Stamford Bridge’s 213-6 in which Zac Keune made 65 not out.
Chris Booth (54no) and Charlie Elliot (40no) took York to 245-4 which proved far too good for Beverley Town despite the efforts of Harry Gamble (50).
Ben Elvidge hit 101 not out for Scarborough but Yorkshire Academy comfortably topped them, Matthew Revis (50) and George Hill (59no) to the fore.
Ishan Abeysekara took 7-40 as Sessay were bowled out for 203 with Matthew Till (61) and Mark Jackson (66) setting the pace before Harrogate crashed out for 128.
Liam Collins (42) was top-scorer as Woodlands passed Pudsey St Lawrence’s 173 to open up a 31-point lead in the Bradford Premier.
Hanging Heaton looked well set when Gary Fellows (51) and Callum Bethel (79) helped set strugglers Lightcliffe a 277-8 target but the visitors responded with spirit and, with Yassir Abbas (73) top-scoring, clinched a two-wicket win.
Callum Goldthorpe (72) set up victory for Bradford & Bingley at New Farnley in spite of the efforts of Luke Jarvis (6-30) and Alex Lilley (49no), while a century stand between Toby Thorpe (32) and Nick Walker (63) ensured Cleckheaton beat Methley.
James Logan’s 5-42 spell and the run out of Simon Lambert (70) were key to Farsley’s win over Undercliffe while despite Will Bates’ 71 not out, Wrenthorpe came up 14 short of Townville’s 220-9 in which Jonathan Booth made 68.
James Stuart (98no) and Bilal Anjam (56) put on 116 as Doncaster Town won at Aston Hall to stay top of Yorkshire South.
Josh Shaw (82) was the star of Wakefield Thorne’s win over Wickersley while Jamie Carrington took 5-40 as Sheffield Collegiate beat Treeton.
Binura Fernando took four wicket and hit 51 for Tickhill but they still lost to Whitley Hall, who had Jack Wood (93 & 4-64) in top form.
Harpreet Singh took 5-18 to clinch Barnsley’s 138-run win over Cleethorpes while Saeed Anwar stood out with four wickets and 89 runs as Elsecar overcame Hallam.
Jack McNamara (75) and Ibrar Latif (58) steered Golcar to 213-7 and even though Jason Grosvenor (62) led Moorlands’ reply, they came up two runs short and lost top spot in the Huddersfield Premiership.
Hoylandswaine took over after Gurman Randhawa (6-21) skittled Shelley for 74.
Ben Raven-Hill (109no) and Jack Cassidy (88no) saw Thongsbridge past Honley’s 248 in which Edward Wilson hit a century while Yaasar Imtiaz (79 & 4-39) was the star of Scholes’s win over Armitage Bridge.
Matthew Weston (87) and Jake Finch (61no) helped Barkisland top Kirkburton’s 223, which included 77 from Toby Booth, while a 5-31 haul from Wasim Qasim was the key to Delph’s win over Broad Oak.
Frederick Walker hit 64 and took four wickets as Almondbury Wesleyans beat Shepley.
Four cheap wickets each from James Davies and Nathan Goldthorpe saw Otley on the way to victory at North Leeds and open a 30-point lead in Aire Wharfe.
Istikhar Hussain rounded off a 6-37 spell with a hat-trick of yorkers as Follifoot beat Collingham.
Nick Cocroft (65no) and Rob Spivey (40no) saw Ilkley to victory at Bilton while Jason Wright (63no) clinched Burley’s first win of the season at Rawdon.
Richard Atkins (78) and Ted Haggas (71no) led Addingham to 310-6 as they beat Adel.