The Hatters suffered a first home league defeat in 17 months as West Bromwich Albion came from a goal down at half-time to win at Kenilworth Road this afternoon.
Town were a League Two side the last time a visiting club took all three points away from Bedfordshire, when Accrington Stanley won by the same scoreline on March 10th 2018.
Harry Cornick netted his first goal of the campaign to put Graeme Jones' men ahead on 15 minutes as the Hatters turned in an excellent first-half display against the side ranked high among the favourites for promotion back to the Premier League after a two-season absence.
But Albion boss Slaven Bilic threw winger Grady Diangana into the fray at the break and within six minutes the West Ham loanee had turned the game on its head, finding the back of the net twice to help bring the Town's 28-game unbeaten home league run to a halt.
Impressed by what he'd seen in the opening two matches with Middlesbrough and Cardiff, Jones made just one change from his last team selection in the Championship, with Cornick coming into the starting line-up after impressing in his two substitute appearances and the Carabao Cup win over Ipswich in midweek.
The 24-year-old forward was selected in place of George Moncur, who dropped to the bench where he was joined by Izzy Brown and Kazenga LuaLua for the first time in the league this season.
The Town lined up with Simon Sluga in goal behind a back four of Martin Cranie, Matty Pearson, captain Sonny Bradley and Dan Potts. Jacob Butterfield anchored the midfield with Pelly-Ruddock Mpanzu, Ryan Tunnicliffe and Callum McManaman, playing against his former club, ahead of him, while Cornick was up front with James Collins.
West Brom had the better of the early exchanges, but it was the Hatters who had the clearest sight of goal - Collins heading McManaman's fifth-minute cross on target, but straight at Sam Johnstone - before the opening goal arrived.
A quarter-of-an-hour had passed when the Town made progress down the right, and Cranie swung in an inviting cross that Cornick met with a bullet header on the run that gave Johnstone no chance.
Cornick was the Town's eighth different goalscorer in the four games so far this season, but Albion attempted to respond quickly, Matt Phillips drifting in from the right but aiming his low shot well wide of Sluga's right-hand post.
Town were starting to impose themselves on the game and McManaman drilled a volleyed cross into the six-yard box that just eluded Collins, before Sluga had to be alert to tip a fierce 20-yard drive from Jake Livermore over his bar.
Albion striker Kenneth Zohore was next to have a go, meeting Nathan Ferguson's right-wing cross with a diving header, but Pearson's presence was enough to prevent him directing his attempt on target, as Sluga watched it sail into the Kenny End.
Tunnicliffe slipped Cornick into the area for the Hatters' next opportunity, four minutes before the break, but Johnstone was off his line quickly to smother, with the rebound off the Town goalscorer falling kindly for the visitors' keeper, who was awarded the goal-kick.
Cornick was soon causing problems on the right again, taking a beautiful cross-field pass from man-of-the-match Butterfield in his stride and arrowing a deep cross to McManaman, who brought the ball under control but couldn't find Collins with his dink into the six-yard box.
Albion boss Slaven Bilic made a change at half-time, taking off Kyle Edwards and bringing on Grady Diangana - and it was the substitute who drew the Baggies level within three minutes, with a shot low into the far corner from 20 yards, then put them in front by diverting Filip Krovinovic's shot past Sluga from close range in the 51st-minute.
Jones reacted by making a double sub of his own, replacing Cornick and McManaman with Izzy Brown and Kazenga LuaLua, whose first involvement was to draw a save out of Johnstone, diving low to his right, in the 58th minute.
Tunnicliffe and Cranie, in the right-back position, started the Town's next swift counter-attack, with the two substitutes carrying the ball through midfield and Brown slipping Potts in on the Hatters' left - but the full-back's low cross was just too far in front of Mpanzu, as the midfielder slid into the six-yard box.
LuaLua was asking questions, the Albion defence standing off him and giving him chance to create, and Potts almost got his head on one cross he stood up from a dangerous position on the right edge of the area.
Albion had a potent striker on the bench, however, and Charlie Austin - signed last week from Premier League outfit Southampton - sent a shot narrowly wide of the upright with his first involvement with ten minutes to go.
He went closer five minutes later, his snap-shot from Diangana's set-up crashing against the post, but the Hatters couldn't take advantage of that let-off to find a way back into a game that was well-managed by an experienced Albion side.
TOWN: Sluga, Cranie, Pearson, Bradley (c), Potts, Butterfield, Tunnicliffe, Mpanzu (Shinnie 75), McManaman (LuaLua 53), Cornick (Brown 53), Collins. Subs: Lee, Moncur, Bree, Shea.
Yellows: Potts, Shinnie
Goals: Cornick 15
ALBION: Johnstone, Ferguson, Ajayi, Bartley, Gibbs, Phillips (Pereira 74), Livermore (c), Sawyers, Edwards, Krovinovic, Zohore (Austin 79). Subs: Brunt, Townsend, Bond (GK), O'Shea
Goals: Diangana 48, 51
REFEREE: Andy Woolmer
ATT: 10,059 (1,033 away)