The Hatters delighted a noisy crowd at Kenilworth Road as first-half goals from defenders Gabe Osho and Tom Lockyer gave them victory over the Wearsiders.
It proved enough for Rob Edwards’ team to overcome a 2-1 first-leg deficit and seal a 3-2 aggregate success.
A Wembley final against Coventry or Middlesbrough awaits on May 27, with Luton targeting a return to English top-flight football after a 31-year absence.
The Hatters got the breakthrough they needed in the 10th minute when Osho tapped home from close range after the visitors failed to clear a Jordan Clark corner.
Sunderland came close to an equaliser three minutes later when Pierre Ekwah saw a flicked effort from Patrick Roberts’ corner saved by Ethan Horvath. The midfielder was sharpest to the rebound but his effort struck the woodwork and penalty appeals from the visitors came to nothing.
Luton came close to a second when Luke O’Nien cleared a Carlton Morris effort off the line after Anthony Patterson failed to hold Alfie Doughty’s cross. The home side threatened again when Morris drew a full-length save from Patterson, who was relieved to see Lockyer’s header drop just wide of his post seconds later.
Morris fired just wide following good work by Elijah Adebayo as the hosts sought to go ahead in the tie, and they did just that five minutes later when Lockyer took advantage of space to head Doughty’s cross past Patterson.
Morris had a great chance to make it 3-0 within 30 seconds of the second-half getting underway when Patterson mis-kicked the ball to him, but the striker blazed over.
This was proving a game too far for a Sunderland side ravaged by injury, particularly in defence, in the closing stages of the campaign - although Aji Alese returned from injury as the game’s first substitute in the 58th minute.
The contest was becoming stretched and Alese produced a timely challenge soon after to deny Adebayo as he lined up a shot, before Roberts rounded off a promising run with a weak shot wide.
The same player fired over with 14 minutes remaining as the Black Cats, who finished 11 points behind their opponents, sought to take the game to extra time.
But they rarely looked like doing so, with Luton’s Cody Drameh the closest to scoring in the closing stages, firing wide of an empty goal in added time after Patterson had come up for a corner.
The final whistle signalled joyous celebrations from the majority of the 10,013 crowd, including a large-scale pitch invasion.