Postecoglou's side were seconds away from being held to a frustrating draw in north London until Son rode to the rescue.
His superb cross provided Brennan Johnson with the chance to fire home in the fourth minute of stoppage time.
It was a welcome boost for Son after he jetted back from the Asian Cup this week following South Korea's shock semi-final defeat against Jordan.
Postecoglou introduced Son and Johnson with 28 minutes left and the duo helped Tottenham maintain their top-four challenge after Pape Sarr's 61st-minute goal cancelled out Pascal Gross' penalty for Brighton in the 17th minute.
Paying tribute to Son for his crucial cameo, Postecoglou said: "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. 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."
Tottenham have moved up to fourth place as they battle to qualify for next season's Champions League.
Aston Villa would go back above Tottenham if they avoid defeat against Manchester United on Sunday, but Postecoglou was encouraged by his players' spirited performance against Brighton.
"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 said.
"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.
"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."
