Maurizio Sarri got the desired reaction, having questioned the mentality of his Chelsea players in the aftermath of Saturday's defeat to Arsenal, as N'Golo Kante and Eden Hazard overturned the 1-0 first-leg deficit before half-time.
Tottenham, without any of Harry Kane, Dele Alli or Son Heung-min in a competitive match for the first time since October 2016, found a response of their own by pegging Chelsea back with Fernando Llorente netting an aggregate equaliser.
The shoot-out opened in nerveless fashion, but Eric Dier blazed over the bar and Lucas Moura shot tamely to Kepa Arrizabalaga's left, leaving David Luiz to steer in and spark raucous celebrations.
Returning Tottenham midfielder Dier clattering into David Luiz before fouling Jorginho set a scrappy early tone prior to the hosts going in front after 27 minutes.
Kante was given ample room to lash a partially cleared corner back towards goal and his shot zipped through the legs of Ben Davies, Moussa Sissoko and Spurs goalkeeper Paulo Gazzaniga.
Hazard was revelling in the freedom of having Olivier Giroud playing alongside him as a specialist target man and he fed Pedro to find the overlapping Cesar Azpilicueta, before continuing his run to coolly convert the Spain full-back's cross.
Danny Rose came on for the injured Davies in between the Chelsea goals and the England left-back played a key role as an improved Spurs levelled five minutes into the second half, with Llorente heading home his delivery from the left.
Llorente was unable to find the clean contact Christian Eriksen's delicious swerving cross deserved – he made way for Lucas in the 68th minute – while Pedro fired too close to Gazzaniga at the end of a frantic Chelsea attack.
Giroud, with Gonzalo Higuain looking on from the stands, passed up a pair of glorious chances in stoppage time and penalties were required for the Blues to book a date at Wembley.
What does it mean? Sarri tough love ploy pays off
Bearing in mind the Stamford Bridge dressing room's tendency to chew up and spit out head coaches, the wisdom of Sarri calling out first his team as a whole and then his star player over recent days appeared ill-advised. But his XI responded with the sort of sharp, tenacious display before half-time that Sarri had wondered aloud might be beyond them, while Hazard showed plenty of his dazzling best. Tottenham's reserves of battling qualities under Mauricio Pochettino, even in the face of a punishing injury list and a lack of reinforcements, should not be questioned any time soon.
Jorginho gets Chelsea on the front foot
Sarri's unswerving commitment to his deep-lying playmaker has invited growing criticism of late, meaning Jorginho's sharpest performance since being ransacked by these opponents in November was particularly timely. The ex-Napoli man's expertise in position is not up for debate, but his passing came at a more agreeable tempo, while no Chelsea player gained possession more often. It was a display capped with a delightfully cheeky kick under shoot-out pressure.
Dire opening from Dier
Operating without a clutch of his leading stars, Pochettino was boosted by Dier being able to make a first start since his appendectomy. But the England midfielder was over-eager during the early stages, giving away needless fouls and failing to provide the assurance Spurs needed in central areas. His trip on Ross Barkley and failure to react to the quick free-kick that yielded Hazard's goal was a moment to forget, although ballooning a penalty into the Chelsea fans was not the best way to erase it.
Key Opta Facts
8 - Fernando Llorente has scored eight goals in his last five starts for Tottenham in all competitions. Deputy. pic.twitter.com/uDLvRpC8Iz— OptaJoe (@OptaJoe) January 24, 2019
- Sarri is the sixth manager to take Chelsea to an EFL Cup final and just the fourth to do it in his first season in charge (after Gianluca Vialli, Jose Mourinho and Avram Grant).
- Chelsea won just their second EFL Cup penalty shoot-out in their last six attempts, with both successes coming at home.
- This was the third time that Spurs have failed to progress from an EFL Cup semi-final having won the first leg, alongside crashing out against Newcastle United in 1975-76 and Arsenal in 1986-87.
- In all competitions, Chelsea have lost none of the 46 games in which Hazard has scored in at Stamford Bridge (P46 W39 D7 L0).
- Kante has scored four goals in 30 appearances for Chelsea in all competitions this season – as many as he netted in his previous three seasons in England combined (four in 129 appearances).