They both scored in the first half to clinch a 2-1 victory over their Yorkshire rivals at Oakwell, as Leeds even missed a penalty after Tom Elliott was fouled by Luke Potter inside Barnsley's box after just 12 minutes.
Striker Elliott took the spot-kick himself but could only watch his effort saved by Barnsley goalkeeper Heinz Muller.
However, Leeds did score from open play 10 minutes later when Hotchkiss' long-range strike took a wicked deflection of defender Rob Atkinson past Muller.
United's lead was increased minutes before half-time when Westlake met Robert Snodgrass' free-kick with a close-range header, and a 2-0 advantage justified the visitors' dominance.
But Barnsley came into the match after the interval when Miguel Mostto pulled a goal back following a defensive error, and though Leeds substitute Peter Sweeney went close on two occasions in the closing stages, the Whites were forced to hang on to protect their lead.
United's starting line-up included Scott Gardner and Ben Parker, who both completed 90 minute run-outs, while Snodgrass played for 67 minutes before making way for Sweeney.
United Reserves: Lund, Gardner, Webb, Milne, White, Hotchkiss, Westlake, Webb, Snodgrass (Sweeney 67), Elliott (Williams 84), Parker.
Subs Unused: Edwards, Darville, Williams.
Striker Elliott took the spot-kick himself but could only watch his effort saved by Barnsley goalkeeper Heinz Muller.
However, Leeds did score from open play 10 minutes later when Hotchkiss' long-range strike took a wicked deflection of defender Rob Atkinson past Muller.
United's lead was increased minutes before half-time when Westlake met Robert Snodgrass' free-kick with a close-range header, and a 2-0 advantage justified the visitors' dominance.
But Barnsley came into the match after the interval when Miguel Mostto pulled a goal back following a defensive error, and though Leeds substitute Peter Sweeney went close on two occasions in the closing stages, the Whites were forced to hang on to protect their lead.
United's starting line-up included Scott Gardner and Ben Parker, who both completed 90 minute run-outs, while Snodgrass played for 67 minutes before making way for Sweeney.
United Reserves: Lund, Gardner, Webb, Milne, White, Hotchkiss, Westlake, Webb, Snodgrass (Sweeney 67), Elliott (Williams 84), Parker.
Subs Unused: Edwards, Darville, Williams.