Parish’s fifth win of the season saw them close the gap on second-bottom Shelley to 10 points with four matches remaining.
Muhammad Ali struck seven fours and three sixes on his way to 62.
Captain Tim Orrell hit 42 at the top of the innings, while Jamie Hardcastle boosted the total with 32 from 24 balls as the Cavaliers were bowled out for 257 in the 47th over.
Sikandar Raza Butt was pick of the Shelley bowlers taking 4-65.
Wickets fell at regular intervals of the Shelley reply.
Butt followed up his efforts with the ball by hitting a quickfire 64 at almost a run a ball in a knock which included five fours and five sixes.
He was ably supported by opener Louis Sykes (35).
Captain Harvey Jones struck 42 not out batting at number eight but he ran out of partners as Shelley were bowled out for 205.
The introduction of Hardcastle swung the game in Parish’s way as he claimed 5-48 from 12 overs, including the key wicket of Butt.
Parish go into a crucial double weekend with renewed hope of avoiding the solitary relegation place and they travel to third placed Thongsbridge on Saturday before entertaining fourth in the table Broad Oak on Sunday.
Moorlands slipped to a 10-wicket defeat at Cawthorne, who will leave the Huddersfield League at the end of this season having opted to join the Yorkshire Premier League South.
David Winn held the Moorlands innings together as wickets tumbled around him as the number three batsman struck 76 not out from 158 balls, including seven fours and four sixes.
Siraj Sajid supported with 43 but Moorlands were bowled out for 176 off the final ball of their 50 overs with opening bowler Kimson Dalzell producing an excellent spell of bowling to claim 5-15 from 15 overs, eight of which were maidens.
Cawthorne openers Lewis Skelly and Iqbal Khan wasted no time in powering their side to victory in 33.2 overs as they produced an unbroken 180-run stand.
Khan stroked 15 fours on his way to 84 not out, with Kelly making 68 not out, while the Cawthorne innings was also boosted by 28 extras including 21 wides as they moved out of the bottom two.
Mirfield suffered a six-wicket defeat away to Upperthong and look set to finish in the bottom two of the Conference.
Beau McGuinness top scored with 83 from 141 balls, which included 12 fours.
Adam Goldthorpe had dominated an opening wicket stand of 46 with McGuinness as he struck 42 from just 32 balls including six fours and two sixes.
Upperthong reached their target in 42.5 overs as Benjamin Earnshaw struck 85 and was supported by opener Greg Marsh (52) and Tom Mighall (33no) to condemn Mirfield to a 15th defeat of the season.