Tian Koekemoer anchored Tickhill’s innings with a carefully constructed knock of 83.
James Waller also chipped in with 30 to help the visitors post 219-9 off 50 overs.
Tickhill skipper Alex Rowland removed Town’s top three to put the brakes on their reply.
Contributions from James Ward (31), Jaden Fell (30) and Charlie Kaye (26) meant Doncaster remained in with a chance but they eventually closed on 195 all out.
Rowland and Josh Court both claimed figures of 3-47.
Overnight leaders Appleby Frodingham lost by two wickets at Barnsley which allowed TIckhill to leapfrog them back into pole position, while Town dropped to seventh in the standings.
Tickhill host third-placed Wakefield Thornes on Saturday and Doncaster travel to Appleby Frodingham.
*Askern Welfare stayed in touch with Division One leaders Oulton thanks to a five-run victory against West Bretton in the Pontefract League.
Reece Gibbon (49) and Ashley Towler (37) were the only two batsmen to really trouble the scorers as Askern limped to 154 all out.
But an excellent bowling and fielding display restricted West Bretton to 149-7 in response.
Oulton, who won by 108 runs at Streethouse, have a 10-point lead at the summit.
Askern travel to bottom side Hundhill Hall, who have lost 11 out of 11 games, on Saturday.