Spurs entered this fixture following a controversial 2-1 victory over Liverpool last weekend, where Jurgen Klopp's side were denied a legitimate goal due to a "significant human error" by VAR operator Darren England.
It meant three points for Ange Postecoglou's team at Luton would send them to the summit for at least 24 hours, but they had to work hard for it after Yves Bissouma was sent off in first-half stoppage-time.
Bissouma was booked twice in quick succession by referee John Brooks, the second for simulation, but Van de Ven's close-range finish in the 52nd minute earned Tottenham a hard-fought win.
The Australian coach said it was a great collective effort for the Spurs.
"Biss made a mistake. He has been brilliant for us this year. He made a mistake and the good thing is how he reacts to these things," Postecoglou said.
"His team-mates made sure that mistake didn't cost us and I'm sure when Biss gets back in the team he will reciprocate and make sure that whatever else happens he can get us over the line. "
Spurs had put seven goals past the other newly-promoted teams this season and should have added to that tally inside 10 minutes.
Luton had the ball in the net after 39 minutes but it was immediately ruled out and a VAR check showed Elijah Adebayo had shoved Cristian Romero.
Luton should have taken the lead two minutes after half-time when Ogbene held off Destiny Udogie and crossed in for Adebayo, but he could not steer his effort on target.
The hosts were hit with a sucker-punch in the 52nd minute when Van de Ven opened his account for Tottenham.
Manchester United substitute Scott McTominay scored two goals in second-half stoppage they rallied to beat Brentford 2-1.
Chelsea's Raheem Sterling made a point to England boss Gareth Southgate as he sparked a Chelsea comeback in a 4-1 win at Burnley.
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