Acomb’s win came on a day where ball dominated bat.
Visitors Stamford Bridge chose to bat and were dismissed for 82, with just wicketkeeper and opener Jack Timby (30) and lower-order batsmen Ameya Joshi (16) and James Keast (19) making double figures.
Darius D’Silva (3-17), Chris Aplin (3-44), Darcy O’Connor (2-5) and Charlie Marshall (2-15) shared the wickets as the innings was wrapped up in the 29th over.
William Robertson (3-24) and Fletcher Coutts (5-39) left Acomb 34-5 and 66-8 before they were seen to a two-wicket triumph by Joe Schofield (9no) and Marshall (5no) after O’Connor had made a crucial 27.
Yorkshire Academy were indebted to Will Luxton (71) and Ben Cliff (28no) for more than two-thirds of their 147 at Dunnington.
Luxton reined in his natural attacking instincts but still hit six fours as George Drury (5-27) and David Brent (3-24) tested the youngsters.
Drury completed a fine match by scoring 39, but the hosts were still 99-6 before Jack Bolam (35no) and Daniel Barrett (19no) combined in a match-winning unbroken stand of 51 to reach their target with 16 balls to spare.
Acomb and Dunnington both have 34 points, and the only other victors in the division were Woodhouse Grange, who were 18-3 before being rescued at home to Sheriff Hutton Bridge.
Chris Bilton (63) and Henry Wilson (57) put on 119 for the fourth wicket in Grange’s 210-8, Freddie Collins (3-57) being the most successful of the seven bowlers used.
The visitors were looking good at 75-2 after a stand of 68 between Mark Fisher (29) and Tommy Hudson (33) but there was nothing substantial after that and the strugglers fell for 173, with Josh Jackson taking 4-53.
Appleby Frodingham and Treeton are both on 42 points and are third and fourth, respectively, in the Yorkshire Southern Premier League after wins.
Treeton’s decision to field at Doncaster proved wise as the home side were ‘castled’ for 92, with just Joe Gallagher (24) and Bilal Anjum (21) making over 20 as Stephen Foster (4-25) and Liam Johnson (3-16) held sway.
Viraj Bhosale (42no) then led Treeton to a five-wicket victory.
Hosts Wickersley made 160-8 after winning the toss and batting but only Jamar Ifill failed in the reply as Appleby Frodingham won by six wickets at the end of the 37th over.
Captain Matthew Fowler (49) and Alex Grimes (26) added 67 for openers, and Kieran Lindley (33no) and Jack Harrison (29no) later put on an unbroken 63.
Along with the Huddersfield League, the Bradford Premier was harder hit by the weather, and only Cleckheaton could squeeze a win in the top flight.
The bottom-of-the-table side used two bowlers in dismissing Bradford & Bingley for 112, with Iain Wardlaw taking 5-56 and Harvey Booth 5-46.
However, rain then meant a Duckworth, Lewis Stern adjusted target of 100 in 29 overs and, chiefly thanks to opener Kris Ward (26), Cleckheaton won by seven wickets with four overs to spare.
The most finely-balanced game that was ruined by the weather was at Townville, who were dismissed for 67 (David Stiff 5-33, James Byrne 4-28) before having Hanging Heaton at 20-3.
Saltaire’s positive cricket again paid dividends at Addingham in the Aire-Wharfedale League in a game that finished long after many others.
Richard Atkins (57) and Ted Haggas (55) helped the home side score a competitive 205-6, and that looked huge when the visitors were reduced to 6-3.
The in-form Jibrael Malik turned the match around with 102 not out off 88 balls, including seven fours and nine sixes.
If the match had run its course, Saltaire may well still have been tested but rain at the end reduced their target to 177 off 35 overs, and Saltaire had already scored 180, giving the Division One leaders a five-wicket win.