The north London team released a statement before the game condemning Erik Lamela, Giovani Lo Celso and Sergio Reguilon after the three were pictured breaking COVID-19 regulations alongside West Ham's Manuel Lanzini.
Lamela and Lo Celso were not named in the team while Reguilon was on the bench.
Kane opened the scoring for Spurs on 29 minutes with a penalty. Steven Bergwijn was brought down by Ezgjan Alioski on the edge of the box and VAR checks confirmed the referee's on field decision to give a penalty.
Son scored Spurs' second on 43 minutes with help from his scoring partner Kane who found space on the right wing. He then crossed the ball to the far side of the box where Son was waiting to tap it in.
The pair have now combined for 13 Premier League goals this season, equalling the record held by Alan Shearer and Chris Sutton from the 1994-95 season.
"Harry and I have been working together a long time so we understand each other really well," Son said after the game.
"I'm really sad that I couldn't give an assist today for H. The ball he played was perfect for me. Sometimes it is telepathy, sometimes we work on it."
The third goal came five minutes into the second half when Son directed a cross into the box and Alderweireld headed it into Meslier who carried it over the line.
"It was a really difficult game," Son added. "They do an unbelievable job and work so hard.
"We created a lot of chances and got a clean sheet, it's a fantastic start to the new year. I couldn't wait [to score his 100th goal for Spurs] and I'm very happy and very grateful for my teammates who supported me early on."
Leeds are in 11th but have at least one game in hand over every team below them.