A week after a last-gasp winner enabled Spurs to see off the nine players of Liverpool, Ange Postecoglou’s team survived the dismissal of Yves Bissouma and a host of Luton chances.
The Mali midfielder was sent off in first-half stoppage time for diving, his second yellow card in barely 10 minutes.
Tottenham were a man down, but not out, and took the lead early in the second half after a quick corner allowed James Maddison to tee up Van De Ven.
Luton did everything but score. Elijah Adebayo should have done even before Tottenham’s opener and the home side had a number of opportunities to equalise.
But Tottenham held firm and extended their unbeaten start to the season to eight games, moving into first place ahead of Sunday’s matches involving their top-of-the-table rivals.
The visitors ended the first half a man down, but should have been at least a goal up.
Richarlison missed two good chances in the opening four minutes, and Pedro Porro also fired wide in the seventh.
Luton gradually gained a foothold in the game but had Thomas Kaminski to thank for keeping it at 0-0 with a fine save from Dejan Kulusevski.
The home fans had grown frustrated with referee John Brooks for giving free kicks to Spurs for almost any physical challenge.
But in the fourth minute of first-half stoppage time, they were delighted.
Bissouma, booked a few minutes earlier for a cynical foul on Chiedozie Ogbene, took a dive but was not touched by Marvelous Nakamba.
Brooks had no choice but to show a second yellow card, and then a red.
Within two minutes of the restart, Luton should have taken the lead. But Adebayo somehow failed to convert Ogbene’s cross.
Punishment soon arrived. Kulusevski quickly took the third in a series of Spurs corners and found Maddison, who beat his man and jabbed the ball back for Van De Ven to force it home.
Luton dominated the rest of the game but could not score, with Alfie Doughty and substitute Cauley Woodrow missing the best of the chances.
Spurs goalkeeper Guglielmo Vicario made a couple of saves but nothing spectacular, as his team ground out a win that maintains their momentum.
