Hill's side produced one of their best performances of the season on Saturday to increase Leeds' woes on their own patch.
First-half goals from Ricardo Vaz Te and the in-form Craig Davies did the damage for the Tykes, who last left West Yorkshire with the points nearly 22 years ago - a result that secured their second-tier survival.
Leeds still went on to secure promotion that season - something chairman Ken Bates has requested from this campaign - but on this showing, and other home performances this term, that is a big ask, even in spite of Ross McCormack's second-period stunner.
Barnsley, meanwhile, continued their steady improvement under former Rochdale boss Hill, to secure a first away since August even though they lost David Perkins to a second yellow card three minutes from time.
Robert Snodgrass, who scored Leeds' goals in the win at Burnley last weekend, had an early run and a shot, but that was the sum of his side's early chances in spite of their possession.
Buoyed by riding the early storm, Barnsley settled into things and, with their passing crisper than Leeds' - particularly from the outstanding Jacob Butterfield - they began to impress.
Captain Butterfield ghosted into the box unmarked and should have done better with a free header, while at the other end, Aidy White was booked for taking a dive over the flailing leg of Jim O'Brien in the box.
The same two players were then heavily involved in Vaz Te's 27th-minute goal, although it was another Leeds player taking a tumble this time.
Lloyd Sam slipped as he tracked a Bobby Hassell throw, allowing O'Brien to get in behind White and square for the waiting Vaz Te, whose scuffed shot looped off the turf and over Alex McCarthy.
McCarthy, signed on loan from Reading after Paul Rachubka's meltdown in the 5-0 defeat by Blackpool, had impressed in his two games for the club so far but an error from him then allowed Barnsley to double their lead two minutes before the break.
Butterfield, famed for shooting from distance, took aim from range once more and, even though McCarthy got his body behind it, he could only shovel it into the path of the onrushing Davies who made it three in two games.
Leeds unsurprisingly looked to up the ante after the break and Snodgrass hit the post with a curling effort that had Luke Steele beaten.
That was all the crowd needed to get back on side with their players and, when McCormack slammed home a delicious 25-yard free-kick with 35 minutes left after a foul on Luciano Becchio, the atmosphere reached fever pitch.
United boss Simon Grayson threw on the lively Ramon Nunez in a bid to capitalise on the momentum, but some resolute defending from the Tykes allowed them to stabilise and, when McCormack was withdrawn, they had ridden out the worst of the pressure.
They could then have restored their two-goal cushion had debutant Nile Ranger got on the end of O'Brien's fizzing cross-shot, while McCarthy was fortunate to see White on hand to clear after he shelled another shot from distance, this time from Matt Done.
Perkins was then sent off, but goalkeeper Steele ensured his dismissal was not costly when he saved in added time from Nunez.