Chelsea were forced into a last-minute formation switch after Thiago Silva and N’Golo Kante tested positive for Covid-19.
Saul stepped up for just his seventh Chelsea start since joining the Blues on loan from Atletico Madrid in September, operating in a more familiar central midfield role in a 4-3-3 system.
And boss Tuchel was left to heap praise on the 27-year-old for finally finding his Stamford Bridge rhythm after almost four months of struggle.
“He has digested his experiences here in the beginning, when he maybe did not expect it to be like this,” said Tuchel. “Now he would certainly not be the first player to struggle with the switch to England.
“But he’s open, fully focused and totally committed to the team. I’m very happy he had a performance like that, which was a huge step forward.”
Chelsea put one foot in the League Cup final with a dominant victory over fierce rivals Spurs, with Antonio Conte enduring a wretched first managerial return to Stamford Bridge.
Kai Havertz netted just five minutes in after Marcos Alonso robbed Emerson Royal deep in his own territory.
Then Ben Davies put through his own net, unwittingly deflecting the ball off his shoulder from Davinson Sanchez’s botched clearing header.
Chelsea suffocated sloppy Spurs but also spurned several fine chances that if converted would have killed the semi-final tie at the midway point.
Saul finally showed his true pedigree with a tenacious and measured midfield performance.
And Chelsea’s German coach Tuchel admitted he has seen Saul start to improve day by day now he has warmed to his west London task.
“He’s more happy, more free in training; I see it every day,” said Tuchel. “He played better when he came on against Wolverhampton. He’s stepping up and stepping up.
“I was so happy when I saw him on the sideline when we scored the equaliser against Liverpool. He was totally involved in the moment, totally committed.”
Conte steered Chelsea to the 2017 Premier League title only to depart a year later after a major fall-out with the Blues’ board.
The former Inter Milan boss pulled no punches in comparing his struggling Spurs side to 2021 Champions League winners Chelsea.
“Look, Chelsea last season won the Champions League,” said Conte, laughing. “And in this season they invested much more money to improve the team. So I think this is enough to understand the difference between us and them.
“We need time, so much time, we need so much time, before trying to resolve the situation. You can resolve the situation in only at least a year. I have a bit of experience, and also speak the facts.
“We need to stay as a unit, and try to rebuild an important situation for Tottenham. If we said the transfer window in January would solve our situation, we’d be telling you a lie.
“You have to see if there are players to improve you, but the resolution now is to work, to improve all aspects of our squad.”
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