The Alderson Drive club were bowled out for just 120 and Barnsley went on to win by four wickets.
Tickhill, who lie second in the Premier Division table, now trail Appleby Frodingham by 18 points after the leaders won by six wickets at home to Whitley Hall.
The top two sides go head-to-head this Saturday at Brumby Hall.
Alex Rowland’s side elected to bat but were in all sorts of trouble at 5-3 before Tian Koekemoer (38) and Connor Fisher (30) steadied the ship.
However, after rebuilding and reaching 80-4 the innings collapsed to 120 all out in 33.2 overs.
Oliver Jackson was the chief destroyer, claiming figures of 5-37.
Koekemoer claimed a wicket with the first ball of Barnsley’s innings and Adi Sreedharan took 4-46 but the visitors patiently edged their way to victory in 32.3 overs.
Tickhill topped the table earlier this month but back-to-back defeats have now left them playing catch-up with seven games to go.
Umar Amin scored a superb 124 not out to help Doncaster Town to an 83-run win at Elsecar.
Amin’s knock included 16 fours and two sixes and saw Town post 257-6 from their 50 overs.
James Keast also hit a quickfire unbeaten 43 and Charlie Kaye made 36.
Elsecar replied with 174 all out as Keast claimed 4-56 with the ball and Amin took 2-19.
Sixth-placed Town host Whiston PC on Saturday.