The Hatters booked a fourth round tie at home to Grimsby with a 97th-minute winner from Elijah Adebayo seeing off Wigan Athletic at the DW Stadium.
Cauley Woodrow had drawn the Town level five minutes into the second half, just moments after Thelo Aasgaard had given the Latics the lead. Then, with extra-time looming, Adebayo volleyed in his second goal in as many games - and fifth of the season - to secure the win.
Manager Rob Edwards made four changes from Saturday's league defeat against West Brom, with Reece Burke and Gabe Osho starting in defence against the Latics once again, as they did at Kenilworth Road ten days ago.
Louie Watson started in midfield with Allan Campbell and Jordan Clark, who wore the captain's armband for the first time, whilst Cauley Woodrow kicked off in a more forward role alongside Elijah Adebayo - who scored his first goal since October at the weekend. Top scorer Carlton Morris missed out after picking up a slight calf injury against West Brom.
Woodrow created space for himself to register the game's first effort on goal inside the opening two minutes, beating his man on the edge of the box before his attempted chip was deflected over for a corner, which the hosts defended well.
The former Barnsley man had a hand in the next opening on 11 minutes, this time heading Watson's deep cross into the six-yard box for Adebayo, whose header was straight at Ben Amos in the Wigan goal, before spurning a great chance himself seven minutes later, nodding Burke's excellent outswinging centre over the bar after good work on the right by Bree.
As the Hatters continued their domination of the opening 20 minutes, Bree was next to have a go, but his curling 25-yard free-kick wouldn't come down enough to trouble Amos.
Wigan posted their first moment of intent on 26 minutes when Town could only clear a corner as far as the edge of the box, where Thelo Aasgaard flashed a low shot through a thicket of legs but wide of Horvath's right post.
Woodrow was at the heart of all the Hatters' attacks, and his inviting low cross from the right edge of the penalty area just evaded Campbell and Adebayo as it zipped across the six-yard box.
Burke was alert at the other end to produce a perfectly timed block as Wigan pressed from a long throw, with Adebayo's attempted clearing header rebounding back off a Wigan head into the danger area as half-time approached.
The hosts broke the deadlock less than a minute into the second half when another long throw from the right was headed to the edge of the area and Aasgaard smashed a volley into the top corner, giving Horvath no chance.
Town were level within four minutes when Bree and Burke combined on the right to free Campbell, whose cross was smashed at goal by Woodrow, only for keeper Amos to puish it straight back to him. The Town forward dug a second shot out, which beat Amos and was hacked clear by a defender, only for Hawk-Eye to rule that the ball had crossed the line.
Wigan made a double change on 63 minutes, replacing their front two of Callum Lang and Ashley Fletcher with Will Keane and Josh Magennis, while Edwards made his first switch at the same time, introducing Harry Cornick for Campbell.
Doughty fired a 25-yard shot on 67 minutes and was clattered by Tom Naylor in the process, requiring treatment with a corner the only reward for the Hatters for the Wigan midfielder's deflection. Moments later it was Naylor going down in the Town box, under challenge by Doughty, but referee Matthew Donohue waved away the hosts' appeals for a penalty.
Adebayo saw a 73rd-minute header blocked, then almost immediately Woodrow played Cornick through into the Wigan box with a delightful chip, only for Wigan sub James McClean to get back to clear off the line, with Amos beaten.
Adebayo hit a shot on the turn as Wigan struggled to clear a deep cross by Bree with ten minutes to go, but Amos saved comfortably, then Woodrow saw an 85th-minute shot blocked behind for a corner after good work in the box by Cornick, before Doughty's attempted curler from the right was headed clear with a minute of normal time left.
Burke became the first Hatter into the referee's notepad for late foul on McClean, and Adebayo reacted well to block Jack Whatmough's goalbound header from the Republic of Ireland international's set piece.
Horvath got his body behind another Aasgaard volley a minute into seven added on at the end of the regulation 90, before Edwards replaced Bree with Tom Lockyer for the closing stages.
After all seven additional minutes had been played, Adebayo scored a dramatic winner with a low finish past Amos, his second in as many matches.
WA - Aasgaard 46
LT - Woodrow 50, Adebayo 90+7
Att: 5,668 (191 Hatters)