Beresford, who had moments earlier made a stunning save from Michael Kightly to keep the score at 2-2, allowed Karl Henry's long-range effort to squirm under his body in the 66th minute and leave Luton deep in relegation trouble.
Town had led 2-1 at half-time after Leon Barnett's header and Lewis Emanuel's 30-yard thunderbolt had cancelled out Gary Breen's opener for the visitors.
But things went wrong after the break as Andy Keogh hauled Wanderers level before Henry embarrassed Beresford with his hopeful strike from distance.
It made it five wins on the spin for the Molineux men, while for Town it means they have just one win in their last 12 league games.
Hatters kept faith with the same 11 that fell to a last-gasp midweek defeat to Norwich, while Wolves made one change to the side that beat Leeds 1-0 in their last outing as Breen replaced the suspended Darren Potter.
The visitors came into the game on the back of a six-match unbeaten run and they dominated from the start with some composed, passing football.
Mick McCarthy's men almost took the lead in the fourth minute when Seyi Olofinjana unleashed a 20-yard thunderbolt after Michael McIndoe had laid off Rob Edwards' right-wing cross, only for the ball to cannon away off the top of the post.
Six minutes later the opener duly arrived as Luton's vulnerability at set-pieces was exposed yet again.
Keith Keane gave away a free-kick 40 yards out near the touchline after a foul on McIndoe and Kightly whipped the ball in for Breen to get the faintest of touches to nod into the far corner of the net.
Kightly looked a threat on the right and teed up Stephen Ward to mis-hit a shot at Beresford in the 12th minute, before Ward then smartly turned and fired a deflected left-footed effort just past the post from 15 yards after McIndoe's cross seven minutes later.
Hatters looked ragged and short of confidence, but they hit back to equalise quite literally with a bolt from the blue.
Kevin Foley rolled the ball across the midfield from wide on the right and Emanuel, pushing up from left-back, let fly with a searing 30-yard strike that flew into the bottom right-hand corner off a Wolves defender for a stunning equaliser.
That woke Town from their slumber and, despite the atrocious Kenilworth Road pitch, Luton played their way back into the match, forcing a number of corners.
It was from their final flag kick of the half in the 45th minute that Barnett rose to power home a ten-yard header from David Bell's centre to give Luton the lead at the break.
Town couldn't build on the advantage after the interval though as Wolves came back into the match and Kightly's right-wing cross in the 52nd minute caused confusion in the home defence resulting in Matthew Spring nicking the ball of Ward's toes in front of goal.
A minute later Wolves were level when Neill Collins found Kightly free in the penalty area and, although his 12-yard shot was superbly blocked by Beresford, Keogh was first to the rebound to net from two yards out.
Luton almost responded when Matt Murray was forced to dive low to his right to keep out Bjorn Runstrom's header from Bell's 55th-minute cross.
But Beresford had to be alert again to deny Kightly in the 61st minute after the Wolves player had jinked past Emanuel and Steve Robinson and fired in a rising left-foot shot from just inside the area.
Beresford's good work was all undone in a horrifying moment five minutes later though as Henry, who along with Olofinjana had bossed the midfield all afternoon, sidestepped Spring and hit a low 30-yarder that somehow eluded Beresford and trickled into the net.
The best Luton could muster after that was a speculative 25-yard effort from Keane in the 80th minute as Wolves comfortably saw out the game.