Spurs went into the match facing a one-goal deficit but they required just 10 minutes to get back on level terms after dominating the opening stages in North London.
Gent failed to defend a long ball sent down the right flank and after making his way into the penalty area, Christian Eriksen slid the ball inside the near post from an acute angle.
Moments later, Alli squandered a good chance from just inside the 18-yard box as he dragged his first-time effort wide but while Spurs remained on top, they conceded an away goal from a corner which should not have been given.
The set piece was floated towards the back post where Stefan Mitrovic rose above the defence, but while his header was not threatening a goal, Kane diverted the ball into the bottom corner.
However, six minutes before the break, they were dealt a huge blow when Alli was correctly sent off for a bad challenge on Brecht Dejaegere, with his studs going over the ball and into the player's shin.
Mauricio Pochettino opted against making any substitutions at half time and it was a decision which appeared justified as his players surged forward at will in the hope of getting back into the tie.
Just before the hour mark, Eriksen played in Kane and the striker should have got on the scoresheet for the second time on the evening, but he lashed his effort wide of the far post.
However, it was not long before Victor Wanyama gave Spurs a lifeline as he found the corner from 16 yards after good work from both Walker and Eriksen.
As Spurs continued to attack, Walker lashed the ball into the side-netting when well placed, but with less than 20 minutes to go, Gent should have wrapped up the tie when Moses Simon was found at the back post, but he sent his free header wide from close range.
The home side introduced Harry Winks in an attempt to speed things up in the middle but with eight minutes left, Gent scored their second goal of the night to all but ensure their place in the next round.
Kalifa Coulibaly broke forward and although his attempted cross was blocked by Eric Dier, the ball fell perfectly for Jeremy Perbet - who scored the only goal in the first leg - to volley into the net from 10 yards out.
In the closing stages, Son Heung-min should have scored after being played in by Kane but the South Korean blasted the ball high over the crossbar from 12 yards.
Kane also curled wide in added-on time but for all their efforts, Spurs eventually tired in the closing stages and must now focus their attention on the domestic scene.