Spurs topped their London rivals 1-0 on Tuesday, opening their semifinal clash with a first-leg victory at Wembley Stadium.
The game's pivotal moment came came in the 26th minute, as Kane fired from the spot for what proved to be the match-winning goal.
That goal was the product of VAR, as Kane was taken down in the box by Kepa Arrizabalaga.
After officials reviewed both the foul and the potential of an offside call on Kane, the penalty was given and Kane buried his kick from the spot.
"I played to the whistle and nicked it round the keeper, it was a clear penalty. VAR is there for a reason and they got it right," the Tottenham captain told Sky Sports following the victory.
"I'll have to watch it back and see. I'm used to it after the World Cup, it's a big part of football going forwards. From our point of view, it doesn't change much [waiting to hear if it was a penalty].
"Chelsea had a point to prove, they didn't play well last time they were here. It was important we won the game going into the second leg."
The goal saw Kane score his sixth in six matches while also setting a new Spurs mark with six 20-goal campaigns.
With the defeat, Chelsea lost their third consecutive match to Tottenham, the first time that has happened since the 1960s.
Spurs previously topped their rivals in March and November, with the fall victory being a 3-1 triumph that helped prove Spurs' title credentials.
Now, Spurs are 90 minutes away from a cup final as they head to Stamford Bridge for the second leg on January 22.
"It was a lot different to the game we played in the league. I didn't play in that one but it looked comfortable for the boys," defender Danny Rose told Sky Sports.
"Tonight was hard work. It was a great team performance, everyone dug in and I think we deserved it in the end. We tried to get the second, but it was one of those games and Chelsea played really well. Now, we take the lead into the reverse fixture in a couple of weeks.
"There is going to be a bit more pressure on them to come out and attack us now, but we are one of the best counter-attacking teams in the league so we are looking forward to it. We won't go there and try to protect the lead, we will play our game."