Anthony Bailey made 23 and Michael Padgett 24 but the hosts were grateful for a fine innings of 61 by Ashley Mackereth as they reached 181 all out in their final over after Chris Smith took 7-61 and Nick Connolly 2-18.
Jamie Sadler replied with 33 for Ossett while Steven Brown made 38 but Parish chipped away as former Ossett paceman Mohammed Shahnawaz claimed 4-59.
Chris Blackburn made 34 not out but he ran out of team-mates as Alex Scholefield (4-38) and Will Atkin (2-16) saw Ossett dismissed for 176 with four balls left.
Batley also chalked up their first win of the season as they triumphed by 89 runs at Scholes.
Opener Mohammed Tahir (68) top scored as visitors Batley reached 190-8. Mohammed Arshad (53) supported, while Ben Burkill claimed 4-46.
The home side made a solid start in reply with Matthew Barnes making 28 but, once he was gone, Batley dominated as nine wickets fell for 40 runs.
Captain Tariq Hussain led the Batley charge with 5-19 in 11.1 overs while Babar Shazad took 3-29 and Tahir 2-8.
Vikram Rathour hit an unbeaten century as Birstall cruised to a 95-run home home win over New Farnley.
Rathour top scored with 103 not out, with his second half-century coming in just 17 balls. He shared a stand of 142 with Paul Marlow (38no) as they made 267-2 after Connor Williams hit 41 and Rob McFarlane 69.
Chris Hill hit 28 and Sean Louw 52 but Farnley never got to grips with a solid Birstall attack. Paul Blakeley took 3-16, Richard Pearson 2-38 and John Carruthers 4-36 put them in charge but Farnley held on to close on 172-9.
Zuigarnain Hiaider fired 66 to set Liversedge on the way to 189-9 at Methley. Steve Blackburn supported with 37 and Will Stiff hit an unbeaten 26 as Mick Waite took 5-51 and Vic Craven 3-39.
Craven led the hosts' reply with 47 before Ryan Bradshaw (60) and Steve Bourne (34no) saw Methley to 191-5 in the 42nd over as Simon Purdy claimed 3-70.
Wrenthorpe lead the table by five points from Townville after beating them by 28 runs.
In Division One, Moorlands won the Mirfield derby at Memorial Park as they beat Hopton Mills by 15 runs.
Alan Sumner scored 40 while Andrew Newby was unbeaten on 50 as the home side were restricted to 131-9. Andy Gray claimed 3-26 and Peter O'Callaghan 3-53 while there was a wicket each for Michael Carroll, Danny Hope and Gary Senior.
Matthew Harrison (2-41) and Danny Pauley (6-40) struck early to reduce Mills to 23-5 and despite 29 from Gray, who was bowled by Greg Sheehan, and a spirited 56 not out by Carroll the visitors were 116 all out in the 34th over.
Buttershaw lead the table by two points after a 24-run success at East Leeds.
Birstall A went top of Division Two as they won a tense game at Woodkirk by two wickets. The hosts were dismissed for 72 in the 35th over as James Tolson (6-19) and Malcolm Ellis (2-14) were among the wickets.
It was then Birstall's turn to struggle as Makool Mulla (4-28) and Garry Dawber (2-4) turned the screw but after being 48-7 Malcolm Ellis (15) and Tolson (9) saw Birstall stumble across the line, reaching 73-8 in 45 overs.
Liversedge A gained their first win of the season, beating Mirfield Parish Cavaliers A by three wickets.
Richard Firth and Christian Webster both hit 21 as Parish were dismissed for 130 by Jamie Hardcastle (5-14), James Hardcastle (2-15) and Ben Cross (2-31).
Jonathan Newsome made 32 in reply but Liversedge were thankful for a solid 52 not out by Jonathan Trevitt to guide them to 131-7.
Batley A lost by four wickets at home to Methley A. Qadir Ghaffoor (48) top scored as Batley were out 118 before Methley eased to 119-6.
Moorlands A are third in Division Three after a 99-run win at Gildersome A.
Adam Roberts (25), Andrew Fortis (26), Ian Lay (20), Tim Meadows (24) and Steven Millington (28) added useful runs as Moorlands A closed on 174-9.
Gildersome struggled in reply and despite the efforts of Hanif Mansoor (21) and Oliver Jefferies (25) the hosts were 75 all out as Andrew Render returned 6-19.
In Division Four, Hopton Mills A had a nine-wicket victory at home to Woodkirk A.
Ilyas Chunara hit 63 and Simon Parkinson 25 as the visitors were dismissed for 125 by David Whitaker (4-25) and Ali Sohal (4-36).
Paul Moorhouse replied with an unbeaten 69 while Ijaz Ashraf made 32 not out as Mills reached 125-1.