Thoresby posted 190 at Ryton Road with Lee Willis hitting 66. Michael Norbury was the pick of the bowlers with 4-32.
Anston’s reply was reduced to 142 all out after Nyeem Ahmed (4-18) and Jobe Shaw (4-35) the pick of the host’s attack.
Thoresby will face Ordsall Bridon in the final after they humiliated local rivals Retford by 165 runs in the other semi-final played on Sunday.
James Brice top scored with 63 as the hosts posted 245 for 8 before Darren Spooner took 5-10 to reduce the visitors to 80 all out in reply.