Mauricio Pochettino’s side trailed 1-0 from the first-leg and they were unable to overturn the deficit despite twice leading on the night.
Christen Eriksen put Tottenham ahead before Gent levelled through Harry Kane’s own goal on the stroke of half-time.
Tottenham midfielder Dele Alli was sent off for a horror challenge after the interval and although Victor Wanyama restored the hosts’ advantage, Jeremy Perbet’s late strike was enough to seal Gent’s upset in front of a new Europa League record attendance of 80,465.
With White Hart Lane being redeveloped, it was more Wembley misery for Tottenham, who had already endured defeats against Monaco and Bayer Leverkusen at their temporary European home which played a major role in their lacklustre elimination from the Champions League group stage this season.
After claiming this week that he can tell whether his team will do well after just 50 seconds of watching a match, Pochettino might have been reassured by Tottenham’s vibrant start.
Meanwhile, a last-minute header from Isaac Kiese Thelin squeezed Anderlecht into the last 16 on away goals where the Belgian side were joined by Ajax and Roma.
Progressing
Anderlecht’s hopes of progressing against Zenit St Petersburg appeared over after the Russians overturned a 2-0 first-leg deficit to lead 3-2 with seconds remaining.
But Kiese Thelin’s decisive intervention earned Anderlecht an unlikely ticket to the last 16 to keep alive their dream of a first continental honour since their 1983 Uefa Cup triumph.
It was the 24-year-old Swedish international’s first goal for the club he joined last month on loan from French Ligue 1 outfit Bordeaux.