The Foxes, who remain bottom and without a win, took the lead through Youri Tielemans’ penalty, but Spurs swiftly turned things around as Harry Kane and Eric Dier scored headers from corners.
James Maddison levelled things up just before the break, but Tottenham moved back in front two minutes into the second-half as Rodrigo Bentancur got off the mark for the club.
From then on, it was the Son show. He scored three goals in the space of 13 minutes, the first two absolutely wonderful finishes, to put an end to his slow start to the season and move Tottenham level on points with Manchester City at the top of the Premier League.
Spurs bounced back from their midweek Champions League disappointment against Sporting Lisbon and ensured they go into the international break on a high.
After his poor start to the season, Son was dropped to the bench by Antonio Conte, though the Spurs boss insisted it was just rotation. Cristian Romero and Emerson Royal joined him among the substitutes.
Leicester took the lead with less than six minutes on the clock in north London, as Davinson Sanchez needlessly dived in and brought James Justin down in the box. Hugo Lloris denied Tielemans at first from the penalty spot, but he was off his line and the Foxes midfielder made no mistake at the second time of asking.
Spurs did not need long to get level, barely more than two minutes in fact. Dejan Kulusevski whipped in a superb cross to the back post from a short corner and Kane headed in his 18th league goal against Leicester.
The visitors’ vulnerabilities at defending set-pieces were once again on show as the home side moved in front for the first time, Dier getting across his man at the near post and flicking Ivan Perisic’s delivery into the far corner.
Despite those goals, Leicester were much the better side as Spurs produced another passive display. They got their reward before the break as Maddison guided a lovely finish past Lloris, and he could have had a second in first-half stoppage time but saw his effort saved.
Leicester were their own worst enemies as Tottenham restored their lead shortly after the break. Wilfried Ndidi was caught on the ball by Bentancur and he strolled through, passing it into the bottom corner with minimal fuss.
The Foxes remained on the front foot, Maddison heavily involved while Patson Daka had a header superbly saved.
For all those bright moments, Spurs’ clinical edge showed. Son got the goal he so badly wanted, driving at goal before finding the top corner with a brilliant effort from 20 yards out. His celebration was one of relief as much as jubilation.
His second came in similarly sublime fashion, this time with his left foot as he found the far corner with a curling effort that left Ward with absolutely no chance.
After he had a tame effort saved by the goalkeeper, Son then did have the ball in the net for a third time. The offside flag initially denied him, but VAR came to the rescue to give the Spurs forward his hat-trick in a truly remarkable cameo off the bench.