Although nowhere near their best, Tottenham led thanks to Ivory Coast right-back Aurier, who scored a freak first goal for the club after 40 minutes with a cross that deceived Brighton goalkeeper Mathew Ryan.
Mauricio Pochettino’s side hit the woodwork twice before South Korea forward Son’s glancing header in the 87th minute was deflected in to seal the three points.
Tottenham remain unbeaten in the league at Wembley since the opening game of the season and, after so much talk of a curse at their temporary home, have now won five of their past six games there.
Brighton, managed by former Tottenham defender Chris Hughton, have hit a rocky patch, taking only one point from a possible 15 to leave them firmly in the relegation fight.
After only three minutes Son had beaten Ezequiel Schelotto on the left and seen a well-hit shot towards the near post blocked by Shane Duffy, and it looked like being an uncomfortable evening for the visitors.
Anthony Knockaert cut in from the right and set off on an ambitious diagonal run that lifted Brighton spirits but when the ball eventually reached Jose Izquierdo, their record signing, his shot looped well over the crossbar.
But they soon found themselves under pressure. Gaetan Bong failed to pick up Aurier as he ran onto a cross and although the Brighton defender blocked the Ivorian’s shot at the expense of a corner, it was a warning that the promoted side could not afford to relax.
In the 25th minute, Erik Lamela, on his first start of the season, just failed to reach a cross from Aurier, and Son scooped the ball high over the bar from a yard or so out after Lewis Dunk and Harry Kane had both missed Harry Winks’s cross from the left.
Brighton had little to offer at that point except dogged defending and some blatant time-wasting.
– Fluke goal –
Tottenham, though, were not as incisive as they can be and shots from Kane and Moussa Sissoko, although on target, caused Ryan few problems.
In the end, it was a fluke goal that broke Brighton’s resistance five minutes before half-time.
Aurier crossed from the right just as he was fouled by Izquierdo, and the impact may have affected the fullback’s aim, as the ball’s flight seemed to be too close to goal.
The referee’s assistant flagged furiously, which may have distracted Ryan, who was unable to prevent the ball dipping past his outstretched hand and into the top corner of the net.
Brighton’s lack of firepower suggested that it would be difficult for them to get back into the game, and they could have been 2-0 behind and down to 10 men after 51 minutes.
Kane’s low shot was parried by Ryan into the path of Son, whose follow-up effort appeared to be blocked by the arm of Duffy, but Son had strayed offside.
Almost immediately a shot by Lamela was deflected onto the foot of the post by Duffy, and the Argentina winger was unlucky again on the hour when flagged offside as a pass from Kane reached him.
Brighton might have equalised with 20 minutes left when a blocked pass fell for Tomer Hemed to hit a volley on the turn but it was too close to goalkeeper Hugo Lloris.
Ryan then turned Kane’s 25-yard free-kick onto the post.
But he could not keep the ball out when Son’s diving header from Christian Eriksen’s free-kick bounced in off Brighton midfielder Davy Propper.
Download our app and read this and other great stories on the move. Available for Android and iOS.