Bilal Anjam’s side ended a run of five straight defeats in all competitions to prevail by 39 runs and move up to seventh in the Premier Division table.
However, Town’s second league victory of the season still left question marks next to their batting as just three of their line-up reached double figures in a score of 192 all out.
Opener Jack Zuurbier batted patiently for 48, overseas star Usama Mir smashed 50 off 32 balls and tailender Sonny Day-Tennant added 13. The next top scorer was 34 extras.
In reply Elsecar looked well poised at 97-3 with Ian Swallow (54) anchoring the innings.
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But the visitors collapsed to 153 all out as Mir, Joel Gunn and Robert Heyes each took three wickets.
Town travel to Cawthorne on Saturday and host Wakefield Thornes on Sunday in the KO Cup.
Tickhill lie tenth in the table following a 78-run defeat at Barnsley.
Royston Dias claimed 4-68 for the visitors but Jonathon Trower (67) and Harpreet Singh Bhatia (67) helped Barnsley post 238-6 from their 50 overs.
Mark Cummins (43) and Joe Billings (33) laid a solid foundation for Tickhill but the innings collapsed from 93-1 to 160 all out.
Ali Jahangir took 4-54 for the home side.
Tickhill travel to Elsecar on Saturday.