The England international was given his marching orders for a shocking tackle on Brecht Dejaegere towards the end of the first half, and although Spurs battled boldly in his absence, they were unable to secure what would have been only a second win in seven matches at Wembley.
Trailing 1-0 from the first leg, Mauricio Pochettino's side made an ideal start when Christian Eriksen opened the scoring with just 10 minutes played, but a Harry Kane own goal put Gent back in front on aggregate.
Alli's dismissal left Spurs with a mountain to climb but they remained the dominant force after the break, and Victor Wanyama restored their advantage on the night with a blistering strike on the hour mark.
Moses Simon spurned the chance to make Gent's progress all-but safe with 17 minutes to play, but Hein Vanhaezebrouck's side - who are eighth in Belgium's top flight - at last booked their place in Friday's last-16 draw thanks to Jeremy Perbet's finish from a counter-attack.
7 – Tottenham have been eliminated from 7 of their last 8 European knockout ties (excl. qualifiers) when losing the first leg. Grind.— OptaJoe (@OptaJoe) February 23, 2017
Pochettino had challenged his players to prove they are ready to perform on the big occasions, and it did not take long for them to level the aggregate scores.
Eric Dier's hopeful punt forwards caused havoc in the Gent defence and Eriksen pounced to slide the ball beneath Lovre Kalinic and into the net from the edge of the six-yard box.
Spurs were firmly in the ascendancy but Wembley was stunned 10 minutes later when Gent snatched a valuable away goal in unlikely circumstances, with Kane heading into his own net as he tried to clear following a corner.
4 - Since the start of 2013-14, Harry Kane has scored 4 own goals in all competitions - twice as many as any other Spurs player. Misguided.— OptaJoe (@OptaJoe) February 23, 2017
The home side's task became that much harder when Alli, frustrated at not winning a free-kick, jumped into an appalling scissor-challenge on Dejaegere to earn a straight red card six minutes before the break.
Undaunted by their numerical disadvantage, Spurs piled pressure on the Gent goal after the break, with Eriksen denied a second only thanks to a timely dash from his line from Kalinic to intercept Kane's clever throughball.
Kane wasted a glorious chance to give Spurs a lifeline, blasting wide of the right-hand post after Eriksen had sent him through on goal, as the home fans around Wembley began to grow frustrated.
Hope was rekindled after 61 minutes, however, as Wanyama fired an unstoppable strike into the top-left corner from the edge of the area after Eriksen flicked the ball into his path.
Kyle Walker came close to a third but Simon missed a clear chance to give Gent a second away goal, heading into the side-netting when picked out unmarked at the far post by Kenny Saief.
Spurs piled on the pressure in the closing stages but Gent made their passage safe in the 82nd minute with their first shot on target, with substitute Perbet reacting quickest to Kalifa Coulibaly's deflected centre to prod the ball beyond Hugo Lloris' left hand and into the bottom-right corner.