Carlton Towers' Richard Watson hit an unbeaten 119 to rescue his side from the early loss of three wickets in their division four clash.
Hartley Heard (31) joined Watson in a stand of 145 for the fourth wicket, which was the highest partnership for Carlton II since they joined the York League.
John Walters took 3-79 for Heslington but then saw Trevor Boddye take 4-15 and Heard complete a personally satisfying day by capturing 5-27 as Carlton took maximum points by dismissing Heslington for 83.
Dogged rearguard batting by Thirsk prevented leaders New Earswick from recording their 14th win and left Yapham with a faint hope of catching the leaders to claim the solo promotion spot.
Mark Benson was Earswick's top scorer with 48, while Peter Stimpson chipped in with 30 as Earswick just missed out on a fifth batting point at 199-7.
On the bowling front Thirsk's Andrew Young took 3-32.
Team-mate Ed Willey then shored up the Thirsk batting line-up as he defied the efforts of Andy Freeman (4-31) to remain undefeated on 30 as Thirsk crawled to a draw at 86-7.
Sheriff Hutton's recent run of success came to an abrupt end when they were whipped out for 84 at Huby, for whom Paul Moore took 4-27 and Chris Cundall 3-12.
Huby's reply was spearheaded by Darren Howell who made 37 not out with Mike South making 25 in an eight-wicket win.
Two struggling sides were in opposition at Tadcaster where resolute defence from the home side denied Sheriff Hutton Bridge a win and deprived them of points which would have lifted them above the relegation cut off.
Home bowlers John Reynolds (3-21) and Matt Keel (3-52) had some success, but good knocks from Steve Clipstone (30), Oliver Wood (41) and Chris Lund (49) enabled the visitors to reach 157-8.
Magnets' achievement in reaching a draw at 98-8 owed much to Peter Dickens, who made 50 in the face of Dave Houldridge who took 4-36 and Dave Ellis who claimed 3-30.
Yapham won their local derby with Pocklington to retain an interest in the promotion race and ensure that Pocklington's relegation jitters remained in motion.
Pocklington were able to secure a handy 174-9 as Mark Croft made 48, Neil Tattersall 30 and Malcolm Harrison 26.
Yapham's Angus Scott and Paul Barnes each claimed four wickets, going for 49 and 43 runs respectively.
Yapham's victorious response came via four batsmen who all made effective contributions.
Adrian Spencer made 37, Barry Pearson 33 and Tim Lazenby 27 before ex-Pocklington player Clive Clark saw Yapham home with five wickets in hand as he made 26 not out.
Bottom team Selby were handily placed to record their third win of the season when they had moved effectively to 41-1 in 12 overs after dismissing Dunnington for 107.
Unfortunately the rain then terminated the action.
Selby's John Burrans had taken 5-8 to put Dunnington in peril.
John Moore (25) and John Fordham (34) were Dunnington's in-form batsmen.
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