Central defenders Gabe Osho and Tom Lockyer got the first-half goals as Rob Edwards' side came through 3-2 on aggregate in front of a passionate, proud crowd under the Kenny lights.
Rob Edwards made just one change to the whole squad, as forward Joe Taylor came onto the bench in place of Luke Freeman.
On loan goalkeeper Ethan Horvath and forward Carlton Morris were both making their 50th appearance for the club, and it was against the backdop of a wall of noise that both teams came out before kick-off.
Town were on the front foot from the off, and although Alex Pritchard fired a free-kick from distance over the bar, the Hatters had the lead by the tenth minute.
The Main Stand roar when Amari'i Bell took a throw on the left almost pushed the ball towards the Sunderland byline, and when Pelly-Ruddock Mpanzu's persistence earned a corner, Clark swung it in and Osho stabbed home from close range after Tom Lockyer won the initial header.
Kenilworth Road erupted, but Sunderland responded and within three minutes Horvath produced a brilliant save to keep out a set piece that came off Elijah Adebayo's head at the near post, with the visitors' appeal for a penalty for handball against Amari'i Bell turned down as the ball ricocheted onto the upright.
The Hatters almost doubled their lead on 22 minutes when Patterson couldn't hold Alfie Doughty's left-wing cross, but Trai Hume got back to hack it off the line, only for the ball to hit Pierre Ekwah and head back towards the goal, with Luke O'Nien completing the clearance
Town were pushing relentlessly and after O'Nien had been booked for a foul on Adebayo, Clark whipped the free-kick in for Morris to head at goal, with Patterson making a good diving save before Lockyer almost netted, only for his glancing header from Adebayo's cross to drift just wide of the far post.
Drameh and Clark combined on the right to set Adebayo racing to the byline, but Morris couldn't steer his effort on target as he got across his man at the near post.
The second goal eventually came two minutes before the break when the Black Cats could only clear another corner as far as Drameh on the edge of the box. For the umpteenth time in the half, the on-loan Leeds right-back picked up the loose ball and fed it back to Doughty, who arced a beautiful cross into the box for Lockyer to head emphatically past Patterson.
Clark was presented with a glorious chance to add a third just 21 seconds into the second half, as O'Nien completely missed his kick, then Patterson attempted to pass it to Lynden Gooch on the left, but instead played it straight to the feet of the Town midfielder, who was well off target with his shot with the goal gaping.
Sunderland survived again, twice, as two Doughty corners from the right - won by some brilliant pressing by Drameh on Gooch - caused concern in the six-yard box as first Ekwah had to divert Clark's flick over his own bar, then Adebayo nodded over from close range in the centre of the goal.
The 10-goal striker then took too long to get his shot away when Morris set him free into the box on the hour, before getting his head on a Clark corner, only for Roberts to head off the line by the post.
The visitors probed, looking for an opening, and after a period of possession where the Hatters couldn't get out of their own half, Roberts cut in from the right and bent a left-footed shot over the bar with 13 minutes remaining.
Adebayo blazed over with just under ten to go after Doughty cut the ball back from another short corner routine, then Edwards made his first change, Allan Campbell on in place of the tireless Clark.
Black Cats' substitute Edouard Michut fired high and handsome as injury-time approached, then Drameh missed an open goal as he raced clear with Patterson stranded after foing up for a corner.
The Hatters had dug in and blocked, chased down every loose pass, left everything out there and deservedly secured their passage to the Arch with a phenomenal display.
Roll on Saturday May 27th!
TOWN: Horvath, Drameh, Osho, Lockyer, Bell, Doughty, Nakamba, Mpanzu, Clark (Campbell 83'), Morris, Adebayo.
Subs: Shea, Potts, Berry, Burke, Onyedinma, Taylor.
Goals: Osho 10', Lockyer 43'
BLACK CATS: Patterson, Roberts, Gooch (77'), O’Nien, Diallo, Clarke, Pritchard (Alese 57'), Neil (Ba 77'), Gelhardt (Michut 64'), Hume, Ekwah.
Subs: Bass, Lihadji, Anderson.
Att: 10,013 (1,036 away)