Yusuf Yazici and Benjamin Andre scored either side of half time to deservedly put Lille 3-2 up on aggregate, only for Matty Cash to give Villa a lifeline with four minutes remaining.
That equaliser was dramatic on its own, yet it was nothing in comparison to what came in the ensuing penalty shootout after extra time failed to separate the sides.
Martinez, already on a booking, received a yellow card for perceived gamesmanship in he early stages of the shootout, but the caution from the game does not carry over to penalties, unbeknownst to the majority.
Argentina's hero from the 2022 World Cup final against France, which resulted in venomous jeers for Martinez throughout, followed saving Nabil Bentaleb's opening spot kick by keeping out Andre's fifth, earning Villa a 4-3 triumph from 12 yards and a spot in the last four.
Villa have no shots in first half
The opening 15 minutes at Decathlon Arena - Stade Pierre-Mauroy passed by without incident, something which suited the visitors, but Lille would soon take the lead with their first notable effort.
Gabriel Gudmundsson got down the left and delivered a threatening low cross into the penalty area, the ball perfect for Yazici to convert first time into the far bottom corner from 14 yards out.
Lille continued to dominate the ball, Villa offering minimal threat going forward, and they were reliant on the ball hitting Emiliano Martinez in the face to prevent Andre's header find the back of the net, the same player then heading wide of the far post soon afterwards.
Although the threat from Lille was not maintained, Villa did not have a single effort on goal throughout the opening 45 minutes.
Cash helps Villa to extra time
Emery would have demanded widespread improvements after the restart, yet Villa almost went behind within a minute after a misplaced pass led to Hakon Arnar Haraldsson drilling the ball narrowly wide from 20 yards.
Villa's first shot finally came in the 56th minute when Moussa Diaby and John McGinn combined to tee up the advancing Matty Cash, only for the right-back to fire harmlessly into the side-netting.
However, that only gave Lille the second wind that led to a second goal. Andre, who had been dangerous in the first half, met an inswinging corner to guide a header into the far corner of the net via the inside of the post, Martinez left with no chance.
Emery introduced Leon Bailey and Jhon Duran but with 10 minutes remaining, they incredibly remained with just one shot throughout the entire match.
That soon changed as Cash forced Lille goalkeeper Lucas Chevalier to tip his long-range strike over the bar, before Bailey's scuffed effort was easily dealt with by the stopper.
With four minutes remaining, Villa got the good fortune that they probably needed. Chevalier collided with a defender when attempting to claim a cross and although Duran's shot was blocked, the ball fell to Cash outside the area who sent a deflected strike into the net, Chevalier still out of position.
In five minutes of added-on time, Bafode Diakite - the goalscorer from the first leg - could have snatched it for Lille, but his header went straight at a grateful Martinez.
Both teams go close before penalties
The opening 10 minutes of extra time offered little in the way of entertainment until Bailey and Douglas Luiz both went close. Chevalier parried Bailey's long-range effort into the path of Luiz, who had half a goal to aim for on the rebound, but his header was too close to the goalkeeper who magnificently clawed the ball over the bar.
After the break, Tiago Santos almost put Lille ahead in the tie with a sweeping shot that just missed the far bottom corner, while Angel Gomes curled a shot marginally off target from distance.
With seconds remaining of extra time, Duran came agonisingly close to winning it for Villa, the Colombia international meeting a terrific Morgan Rogers cross with a shot that was superbly blocked by Chevalier at his near post.
That set up the controversial shootout which was dominated by Martinez. Bailey missed Villa's fourth effort to set up a sudden-death scenario, but after Luiz kept his composure with the fifth, Martinez ended the game in the spotlight with a save from Andre, ensuring that English football have a representative in the last four of European football's three competitions.