The match, postponed by 24 hours due to a waterlogged pitch at the Stadio Jose Alvalade, looked set to be settled in the hosts' favour by Zakaria Labyad's 64th-minute strike, but there was late drama with two goals and a red card in the final 11 minutes.
Gyorgy Sandor equalized for Paulo Sousa's Videoton with an 80th-minute penalty, only for Valentin Viola to swiftly head the Portuguese side to a 2-1 win.
Sandor was then dismissed for a foul on Diego Capel, which ended the Spanish winger's involvement in the game, and there was no way back for the visitors.
Sporting headed into the clash already certain of finishing bottom of the pool after taking just two points from their first five games, while third-placed Videoton's hopes of becoming the first Hungarian club to qualify from the group stages of a major UEFA competition were extinguished when Genk and Basle drew 0-0 last night.
Sporting's Marcelo Boeck was much the busier of the two goalkeepers in the first half, parrying Filipe Oliveira's right-footed blast in the 17th minute and keeping out Nermanja Nikolic's close-range effort with his feet soon after.
Boeck was powerless in the 24th minute, though, when Renato Neto lashed a shot from the edge of the box against the bar.
Despite having been on the back foot for much of the first period, Sporting had a fine chance to open the scoring 10 minutes before the break but Viola directed his header wide from Labyad's free-kick.
Franky Vercauteren's side continued to look more positive after the interval, however, and they received their reward in the 64th minute, when Labyad was on hand to despatch the rebound into the top-right corner after Videoton goalkeeper Tomas Tujvel had parried a fierce drive from Emiliano Insua.
Labyad could have grabbed a second goal eight minutes later but was denied by the feet of Tujvel. The save looked to have proved crucial soon afterwards when Sporting midfielder Fito Rinaudo handled the ball inside his area and Sandor made no mistake from the spot.
But Sporting were back on level terms for only three minutes before Viola's header made it 2-1 following a goalmouth scramble, and the visitors' hopes of getting back into the game suffered a setback a minute later when Sandor saw red for a bad foul on Capel.