Kai Havertz gave Chelsea an early lead when he ran onto Marcos Alonso’s through ball and fired home with Davinson Sanchez unable to keep the shot out on the line.
The Blues’ second was a comedy own goal as Japhet Tanganga headed the ball into team-mate Ben Davies’ shoulder and it flew into the net.
Romelu Lukaku, back in the team after a one-game exile for comments he made in an interview, had several chances and headed wide from close range.
Spurs, who changed to a back four after a torrid first half, had to wait until the 50th minute for a shot, with Harry Kane’s free-kick saved by Kepa.
But the chances continued to come for Chelsea with Hugo Lloris denying Lukaku, Hakim Ziyech and the returning Timo Werner.
Spurs will need to be much better in a week’s time in the second leg to have any chance of reaching Wembley.
Liverpool and Arsenal play in the other semi-final with their games on 13 and 20 January after the first leg rearranged because of Covid cases in the Liverpool camp.
Conte’s Spurs some way off still
Tottenham have looked much improved since former Chelsea boss Antonio Conte replaced Nuno Espirito Santo, only losing once in 11 games before this.
But the wait for a first trophy since the 2008 League Cup will surely go on – with many problems of their own making at Stamford Bridge.
Emerson Royal did not control a pass from Tanganga and Alonso nipped in to set up the opener.
And the second saw Ziyech swing in a free-kick with Spurs’ defenders doing the rest for him.
Most of the pre-match chat had been about Lukaku, who has apologised for an interview which saw him dropped for Chelsea’s draw with Liverpool.
He was involved on plenty of occasions, with several shots – including an effort straight at Lloris in injury time – and a good pass to Ziyech which the Moroccan should have finished.
Encouraging too was the return of Werner after injury, although he replaced Havertz, who broke his finger while scoring the opening goal, at half-time.
The only real downside for Thomas Tuchel’s side, who played 4-4-2 because of a lack of defensive options, is that they did not score with more of their 19 efforts to wrap up the tie.