Umar Amin struck 83 to anchor Town’s innings and see them up to 184 all out.
Matthew Tyas caused problems for the visitors and claimed 5-29.
Collegiate set about their reply in patient fashion and completed victory in 47.2 overs for the loss of four wickets.
George Bartlett made 66 from 134 balls and Shaaiq Choudhry faced 111 balls for his unbeaten 73.
Seventh-placed Town host Cawthorne on Saturday.
Tickhill dropped a place in the Premier Division standings to third following a disappointing 44-run defeat at home to bottom side Whiston Parish Church.
South African star Tian Koekemoer again stole the show but his exploits with bat and ball could not prevent Tickhill losing for only the second time this season.
Koekemoer, who recently claimed an incredible 10-wicket haul, this time captured 6-46 to help restrict the visitors to 183 all out in 50 overs.
He then made 42 not out but ran out of partners as the hosts slid to 139 all out.
Jim Morgan (41) and Connor Fisher (17) were the only other Tickhill batsmen to reach double figures.
Joe Norbury took 4-30 for Whiston PC.
Tickhill travel to Sheffield Collegiate on Saturday.
Sprotbrough suffered an agonising seven-run defeat at home to Houghton Main in the Championship.
Ashley Langdale (4-62) and Sandrian Ward (3-40) impressed with the ball as Main posted 212-9.
Ward then smashed 88 off 63 balls but became the ninth wicket to fall with another 31 still required for victory and it proved to be beyond the final pair as the innnings closed on 205 all out.
Conisbrough also suffered a narrow 16-run defeat at Shiregreen.
Shiregreen amassed 236-7 but Will Scott (58) and Buddhika Sanjeewa (57) gave Conisbrough hope before the innings closed on 220-9.
*Doncaster Town started their YCSPL T20 Blast campaign with convincing wins against Wakefield Thornes and Sheffield Collegiate.
Tickhill, however, suffered defeats against Barnsley Woolley Miners and Cleethorpes.