Billy Paynter put United ahead, only for the Blades to level before the break - ahead of Sam's decisive strike.
Midfielder Adam Clayton played his first game since returning from League One outfit Peterborough United on loan, while Ben Parker, Neill Collins, Richard Naylor and Fede Bessone featured in a strong back four.
Mike Grella and Ross McCormack also got a run-out, with Jordan Snodin - son of ex-Whites captain Ian - coming on as a sub for Grella.
Leeds: Higgs, Bessone, Naylor, Collins, Parker (Baxendale), Clayton (Turner), Hatfield (Thompson), Grella (Snodin), Paynter, McCormack, Sam.