The Hatters had stunned Norwich to make the fifth round three weeks ago, and at times they looked more than capable of pulling off another big upset against a side ranked 67 places above them in the league ladder.
Andre Gray and Luton's match-winner from the previous round Scott Rendell combined well up front, but they could not find a way past David Forde and claim a victory that would have made them the first non-league side to make the last eight in 99 years.
Hulse, on loan from QPR, took his first strike for the club well, hooking the ball over Mark Tyler from a tight angle after Henry had put the Lions ahead following a mistake by Jonas Kovacs. N'Guessan sealed the win with five minutes left.
The win means Kenny Jackett's side go into the hat for Sunday's quarter-finals for the first time since their club-record run to Wembley nine years ago.
Buoyed by their raucous support, Luton started the match strongly. Gray played a clever one-two to open up some space in the Millwall box, but David Forde saved well from the lively striker. The Lions raced straight up the other end and Hulse got in behind the Luton defence but he was unable to beat Tyler.
That proved to be Millwall's only chance of the opening 10 minutes as the underdogs continued to pile on the pressure. Gray slipped past Nadjim Adbou to enter the Millwall box but he shot at the near post when it would have been better to pull the ball back to the hordes of Luton players who were waiting.
Gray, and the impressive JJ O'Donnell, raised the hopes of the home fans, but the visitors then took the lead through Henry.
Janos Kovacs mis-judged the bounce of an aerial ball and the forward raced through and rounded Tyler before slotting home from an acute angle.
Luton threw everything forward looking for an instant reply. Arnaud Mendy went close with two efforts, but the Hatters lacked Millwall's shooting ability.
Hulse tested Tyler with an acrobatic effort and the journeyman striker then made it 2-0 10 minutes before the break, hooking the ball over his shoulder from a tight angle after the ball had bounced around the home box.
Luton came out full of energy after the restart, but Millwall stifled their attacks with some stubborn defending. A deflected shot dribbled in to Lions striker Andy Keogh's path with 25 minutes to go, but Tyler came out to deny the Republic of Ireland striker.
N'Guessan covered 50 yards in quick time on a rapid Millwall counter before laying the ball off to Alex Lawless, who found Hulse at the back post but he tried to square when the better option would have been to go for his second.
N'Guessan made sure of the win five minutes from time when Tyler spilled John Marquis' shot and he turned home from close range.