Manager Simon Grayson had demanded the right reaction after Tuesday night's poor show at Gigg Lane and Leeds went ahead in the fifth minute when Robert Snodgrass fired home after good work by Luciano Becchio.
Impressive summer signing Lloyd Sam crossed for Becchio to head home Leeds' second in the 40th minute and Bradley Johnson outjumped the home defence to convert Jonny Howson's cross just before the break.
Sam and Howson combined well after the restart and the latter smashed home a shot off the inside of the post for the visitors' fourth.
Leeds rounded off the scoring in the closing stages when Becchio headed home his second of the game from Snodgrass' pinpoint cross.
Hartlepool's best effort came on the hour-mark when Gary Liddle's towering header came back off the crossbar, while Andy Monkhouse saw his long-range drive well-saved by Leeds goalkeeper Shane Higgs.