Son, who shared the league's Golden Boot for most goals last season with Liverpool's Mohamed Salah, was left out of the starting line-up after going eight games in all competitions without a goal.
The South Korean responded to being dropped in emphatic fashion, scoring three times in 14 minutes after coming on in the 59th minute to replace Richarlison.
"It was an amazing feeling," Son told the BBC after the win. "I couldn't believe it (when I scored). All the frustration and what I had, disappointment and negative feeling just went. I couldn't move so I stood still. It made me really happy.
"Football is crazy sometimes. Sometimes the ball didn't want to go inside and three times (it did today). It changes everything. I learned so much in this tough period. I need to work hard every time to get the chance.
"Three lucky goals and I'm really proud."
The victory lifted Tottenham level on 17 points with champions Manchester City although Arsenal can regain the top spot if they beat Brentford later on Sunday.
