Chasing 152 for victory, Town were cruising at 71-1 before a five-wicket spell from Will Street reduced the visitors to 95-7.
The experienced Stuart Guy (22no) held firm and combined with tailenders Ben Stoves and Sonny Day-Tennant to see Doncaster home with two wickets to spare.
Earlier Umar Amin and James Keast had each claimed three wickets to help bowl the home side out in 37.1 overs.
Town also beat Nottinghamshire Premier League side Papplewick and Linby on Sunday in the ECB National Club Championship.
Joe Gallagher top scored with 68 to see Town up to 202 all out before then taking 3-17 to help restrict the hosts to 131 all out. Charlie Kaye also claimed 3-15.
Doncaster were denied a clean sweep of wins over the bank holiday weekend as they lost to Cawthorne by six wickets in the Yorkshire Leagues KO Cup on Monday.
They host Elsecar on Saturday in the YCSPL Premier Division.
Tickhill inflicted a first defeat of the season on Whitley Hall and moved up to fourth in the Premier Division table in the process.
The Alderson Drive club were indebted to overseas all-rounder Tian Koekemoer and Nottinghamshire youngster Dane Schadendorf for two match-winning performances.
Koekemoer claimed 5-64 to keep Whitley Hall down to 229.
Schadendorf then anchored a successful chase with a fine innings of 115 and he was supported by Koekemoer (43).
Tickhill won by six wickets with 3.5 overs to spare.
Alex Rowland’s side were knocked out of the ECB Club Championship on Sunday when they lost by 19 runs at Derbyshire side Denby.
Tickhill also suffered a resounding 151-run defeat at Whiston Parish Church on Monday in the Yorkshire Leagues KO Cup.
They travel to Barnsley Woolley Miners on Saturday.
Sprotbrough lie third in the early Championship standings following a 42-run win over Wath.
Harry Graham (90), Dean Williamson (51) and Sadrian Ward (38) got them up to 231-6.
Ward then snared 6-44 to help restrict Wath to 189 all out.
Conisbrough suffered a third straight defeat as they lost in emphatic fashion at Hallam.
Nick Dymock’s magnificent 181 powered the hosts up to a huge score of 335-5.
Shellshocked Conisbrough were bowled out for 154 in response.
Askern Welfare were involved in a dramatic tie with Hemsworth Miners Welfare in Division One of the Pontefract & District League.
Tailender Josh Gillies top scored with 32 in Askern’s below par total of 154 all out.
Hemsworth appeared set for victory at 152-7 before Gillies removed Max Heritage and then, with the scores level, panic set in and Sachira Madapatha struck with two run outs.
Scott Exley made 80 for Hooton Pagnell but could not prevent a 66-run defeat at Kippax.