A whimpering performance from Mike Newell's men saw Town fall behind to Brian Howard's early goal before Martin Devaney's last-minute strike sealed it for the visitors.
A truly woeful first-half display was at least followed by periods of possession after the break, but the Tykes were rarely troubled as they secured a vital win in their attempts to beat the drop and move to within two points of Luton.
The Hatters made two changes to the side that lost 3-2 to West Brom in their last outing as Leon Barnett returned from suspension at centre-half in place of Russell Perrett, while Richard Langley was preferred instead of Ahmet Brkovic meaning David Bell moved to the right of midfield.
Dean Kiely in goal was playing the last game of his current second month's loan spell from Portsmouth.
Barnsley made four changes to the side that lost to Southend in the FA Cup third round replay in midweek, as Manchester United loan man Adam Eckersley, Anthony Kay, Marc Richards and Grant McCann all came into the side.
Lewis Emanuel's early blocked cross-shot and a hopeful 20-yarder from Marc Richards for Barnsley were the only moments of note before the Tykes took a shock early lead.
Luton fans have been used to Steve Howard banging in the goals at Kenilworth Road over the years, but it was a different Howard, Barnsley's Brian, who got the game's opener in the seventh minute.
Both sides gave the ball away in the middle of the park before Devaney, Richards and Daniel Nardiello combined for the latter to deftly play in Howard, who strode into the left-hand side of the penalty area and stroked home left-footed into the far corner from 15 yards.
With Luton seemingly unaware that the game had actually started, Barnsley came again as Nardiello profited from Chris Coyne's miscontrol, and then played the ball in behind for Richards to easily outstrip the Town skipper and fire in an angled 20-yard effort from the right that Kiely dived to save.
Town were then forced into an early change in the 22nd minute as Warren Feeney limped out of the action to be replaced by Adam Boyd.
But that didn't immediately change the flow of the game as Barnsley threatened again with a curling, 30-yard free-kick that Kiely had to tip over.
Luton finally mustered an attack on the half-hour when Dean Morgan chested down Coyne's long ball, but saw his shot blocked by visiting skipper Paul Reid.
And a minute later Town finally registered their first attempt on target of any nature when Langley's optimistic 22-yard shot from the left corner of the penalty area was deflected into the arms of Nick Colgan.
Buoyed by that opening, Luton pressed again and, after Eckersley fouled Boyd on the edge of the area, Morgan curled his 20-yard free-kick into the side-netting.
Another free-kick offered Luton their next chance for a strike on goal five minutes before the break, but Bell arrowed his 25-yard effort from Emanuel's touch, just a yard too high of the target.
The half ended with the Tykes on the offensive as Devaney fired in two free-kicks from wide on the left which Kiely firstly tipped over and then watched fly over the bar.
Luton began the second period with another change as Ahmet Brkovic came on for Sol Davis, meaning Emanuel dropped to left-back, but it didn't stem the Barnsley tide as the visitors came again with Nardiello feeding Howard to blaze a shot high and wide from 18 yards in the 48th minute.
Town then had to make another enforced change in the 53rd minute as Barnett, who had probably been their best player up until that point, departed clutching his ankle to be replaced by Russell Perrett.
Barnsley began dropping deeper and deeper as they settled to cling on to their slender lead and Town began to boss possession without creating clear-cut openings.
Morgan flashed a 20-yard shot wide in the 55th minute, Langley hit a 20-yarder at Colgan a minute later and Boyd then tested the Irishman with a tame 15-yard effort just before the hour mark.
Luton kept plugging away and Robinson almost found the net in the 70th minute when his stinging 20-yard drive was pushed aside by the diving Colgan.
As the groans grew in volume from the home fans, Town's ineptitude was summed up in the 79th minute when Langley stepped up to blaze a 22-yard free-kick high and wide.
Barnsley sealed the win with a breakaway in the final minute when Sam Togwell crossed from the left for Devaney to take a touch before rifling home from a tight angle on the right of the penalty area.