Spurs looked set to drop more points after they had been held to a 2-2 draw at Everton last weekend but Brennan Johnson struck in the sixth minute of stoppage time to fire them back into the Premier League top four.
Son created the winner with a wonderful delivery across the face of goal on his first appearance since he returned from the Asian Cup, where his nation South Korea suffered semi-final disappointment.
Postecoglou introduced Son and Johnson with 28 minutes left and the duo eventually helped the hosts earn all three points after Pape Sarr’s 61st-minute goal cancelled out Pascal Gross’ opener for the Seagulls from the penalty spot after 17 minutes.
“Obviously Brighton were doing really well but they were working really hard to stay in the game and you know they’re going to get tired,” Postecoglou explained.
“The fact we could bring on two attacking players who are going to be a threat, it maybe looks simple but that ball that Sonny plays, that’s a world-class player in a clutch moment.
“Even Brennan getting on the far post, we’ve helped him to do that.
“It’s not about confidence, I feel like with the squad we have for today and hopefully moving towards, we do have that ability irrespective of where the game’s at, to finish games strong.”
On Son, Postecoglou continued: “Maybe the nation he plays for works against him but I think he’s a world-class player.
“You look at his record in the Premier League, the toughest league in the world, his goal contributions irrespective of how the team’s gone through the time he’s been here have always been right up there.
“Even this year, before he left, I think he was probably the best attacking player in the competition, just my opinion obviously. Certainly he’d be up there.
“He’s a world-class player. I thought we did well to cover his absence.
“Richy (Richarlison) obviously stepped up in terms of goal threat, and a few other players, but to have a world-class player for the run-in is brilliant for us.”
Brighton were crestfallen at full-time and deserved more in the absence of Roberto De Zerbi, who was back in Italy recovering after he had invasive dental surgery this week.
Andrea Maldera patrolled the touchline in his absence and watched Brighton go ahead via a Gross penalty after Danny Welbeck had been fouled in the area by Micky van de Ven.
It could have been 2-0 before half-time but Guglielmo Vicario saved Kaoru Mitoma’s poked effort and Spurs finished strongly before Sarr equalised when he curled home after Lewis Dunk deflected his cross onto the post.
The points looked set to be shared after Welbeck fired wide with 14 minutes left but Richarlison sent Son away and he squared for Johnson to slam home with seconds of the six minutes of stoppage time remaining.
“Yes, to concede a goal in the 96th minute in transition away, it is very tough, but this is our mentality,” Maldera said.
“We want to score always the second goal. We don’t think to stay in our half.
“Yes, we can do better but the last pass, Son is a big player, but until that moment we played a big match, with big courage.”