The Wednesday old boy forced Tommy Spurr to slide the ball past his own goalkeeper to put Town 2-1 up in the second period after Fulham loan man Bjorn Runstrom had cancelled out Deon Burton's opener in the first half.
Glenn Whelan's rocket drew the Owls level on the hour only for Talbot to bag the winner with a sharp piece of opportunism minutes later.
His night ended on a sour note personally as he limped off injured in the 67th minute, but Hatters were just grateful to earn a first Championship win in nine matches in their battle against the drop.
Sol Davis' Saturday sending off in the 0-0 draw at Stoke and Russ Perrett's knee injury in the same game meant call-ups for Lewis Emanuel and Keith Keane.
With Town still unsuccessful in their attempts to sign Everton teenage striker James Vaughan on loan, Talbot returned from illness to face his former club in place of Adam Boyd.
Sheffield Wednesday meanwhile made two changes to the side that drew 1-1 with Burnley in their last outing.
The Owls almost got off to a flying start a minute in when their new signing Jermaine Johnson picked up a loose pass from Talbot and ran fully 70 yards past three Luton players before poking a 16-yard effort past a shocked Marlon Beresford's right-hand post and wide.
Seven minutes later Burton and Steven MacLean linked up, freeing Chris Brunt on the left to cross low for Kenny Lunt to slide in with a six-yard effort that Beresford instinctively pushed aside.
The visitors looked dangerous and opened the scoring in the 25th minute when Johnson found Frank Simek overlapping on the right and, from the American's deep cross, Burton nodded home at the far post.
Hatters fans were growing restless, but finally had something to cheer in the 33rd minute when Town levelled as Mark Crossley could only half-punch clear Dean Morgan's corner and Keane drilled the ball back in for Runstrom to prod home from six yards.
Wednesday still threatened though and Johnson showed his pace again four minutes before the break when he left Emanuel for dead from MacLean's pass and scorched an effort over from 18 yards.
Town reshuffled at the interval bringing on Richard Langley in place of the ineffective Morgan. Nine minutes later Luton went ahead when Lee Bullen embarrassingly mis-kicked on the right touchline allowing Talbot to race and cross low and hard for Spurr to slice past his own keeper.
The lead was short-lived though as Spurr partly redeemed himself by teeing up Whelan to slam home an unstoppable 25-yard thunderbolt into the top corner for the equaliser.
Luton didn't panic and went ahead once again three minutes later as Dean Bell's corner was only cleared to the edge of the area to Matthew Spring who nodded on for Talbot to flick the ball over the advancing Crossley and coolly slide home into the empty net.