Brazil winger Willian, selected from the start as star man Eden Hazard was rested on the bench, netted a trademark free-kick in the fifth minute and restored Chelsea's lead from the penalty spot after Harry Kane headed Spurs level.
Dele Alli netted a second equaliser after the break and a Chelsea defence featuring Nathan Ake – making his first appearance against top-flight opposition after returning from a loan spell at Bournemouth in January – were forced to stand firm under sustained pressure.
Hazard came on for Willian to devastate Mauricio Pochettino's men with a clinical finish 15 minutes from time and Nemanja Matic sealed a place in the final with a spectacularly vicious long-range effort.
Chelsea are four points above Tottenham at the Premier League summit, their title charge having been underpinned by Conte sticking largely with a tried and tested first XI.
But with Southampton up next at Stamford Bridge on Tuesday – Spurs have an extra day to rest before facing Crystal Palace, much to Conte's chagrin – the Italian felt it was time to call upon men he wants to feel part of Chelsea's bid for glory.
What a difficult game and what a result! Up to the final now thanks for the fantastic suport pic.twitter.com/ZSPsjZ7n3X— Nathan Ake (@NathanAke) April 22, 2017
"It's important for his confidence, the same for Ake who is a young player from our academy. We must be proud to see his commitment and to see the level that he played at in this type of game.
"It's not easy, honestly, for Ake to go and play his part. I trust every single player and I think today I showed this.
"I'm pleased for Willian because he showed himself to be in good form. For him, this season wasn't easy for many reasons (Willian's mother died last October following a battle with cancer) that you know and I don't want to repeat.
"I must be pleased because I think that in this game I involved all my players in our idea and in our football. This is very important in this part of the season that every single player feels they are part of this project.
"When you work very hard, went you work only with your players every day... don't forget that for me every single player, I work with him in the same way whether he is in in the starting XI or stays on the bench