Last year’s Twenty20 finalists Church made it two wins out of two in Group A after Friday’s 13-run win over Enfield.
Levi Wolfenden’s unbeaten 53 and Nasser Hussain’s 37 was the mainstay of their innings as they finished on 136-4.
Enfield pro Werner Coetsee top scored with 43 and Joe Wrigley chipped in with 38 but they were bowled out for 123.
Accrington moved into second spot after their nine wicket victory over Rishton, who are rooted to the foot of the table.
It was Jimmy Bibby’s last game as a single man before his wedding last Saturday and, while the Rishton captain made 26 and sub pro Roy Silva 29 on his return to his former club, they could only set 114.
Stuart Crabtree’s unbeaten 54 off just 41 balls, Mitch Taylor’s 31 and pro Ashar Zaidi’s quickfire 27 off just eight balls saw Accrington to a comfortable win as they look to reach the last four.