Cleckheaton’s Mohammad Zaman hit a second century of the season before his side were thwarted by the rain in Saturday’s All Rounder Bradford Premier League game.
Cleckheaton were struggling on 50-4 before Zaman helped them recover to post a useful 175-7 in a match reduced to 34 overs.
Zaman’s impressive knock of 104 not out included seven sixes and five fours.
But just 12 overs of the Morley reply were possible when rain saw the match abandoned with the home side on 62-3.
The six points Morley earned enabled them to climb out of the relegation positions by a single point, with Cleckheaton picking up seven points to stay in sixth place.
Pudsey Congs have taken Morley’s place in the bottom two after suffering a six-wicket defeat at New Farnley in a 25-over contest.
Former county all rounder James Middlebrook made an unbeaten 71 as New Farnley overhauled the Congs’ total of 137-4 with 15 balls to spare.
He struck three sixes and eight fours as New Farnley got home despite the efforts of left-arm spinner Nick Lindley (4-36).
Captain Gareth Phillips (51) and opener Callum Geldard (37) were the top scorers for Congs who have nine games in which to pull themselves out of danger.
Bottom-team Scholes looked to be closing in on a third win of the season before the rain wrecked their hopes of defeating Lightcliffe and closing the gap on Congs and Morley.
Left-armer Christian Jackson (5-53) and captain James Stansfield (3-36) bowled impressive spells for Scholes as Lightcliffe, who are just six points above the relegation trapdoor, were dismissed for 135.
Lightcliffe captain Alex Stead was again the top scorer with a determined 65.
Scholes were well placed at 99-4 when play was abandoned, with Irfan Amjad unbeaten on 43.
The abandonement, in which Scholes collected eight points, laves them 32 points adrift of Congs.
Bradford & Bingley and East Bierley, two sides hoping to pick up a win to pull clear of the relegation zone, saw their match rained off when it looked to be heading for a interesting conclusion.
Play was abandoned with Bradford & Bingley on 64-1 in reply to East Bierley’s total of 150.
Opener Charlie Best (41) had given Bingley a brisk start to their reply, while Fahid Rehman (33) and Bjorn Taylor (32) were the main contributors for East Bierley.
Left-arm spinner Noman Ali claimed 5-46 to help dismiss Bierley.
Bierley take five points from the game and are two points ahead of Congs, with Bingley a further six ahead after they collected eight points from the match.