Andy King's header in the second period of extra-time saw Leicester through to the fourth round of the Capital One Cup after a 2-1 win over West Ham at the King Power Stadium.
The tie looked destined for a penalty shoot-out until King, captain for the night, guided a Christian Fuchs cross into the top corner of the net and beyond Adrian, who had kept his side in the game with a string of saves.
Foxes academy product Joe Dodoo marked his full home debut with the opening goal after six minutes, his fourth in the competition after his hat-trick at Bury in the previous round, but West Ham equalised before the half-hour mark through Mauro Zarate's deflected shot.
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Leicester spurned numerous chances to win the game in the second half but found Adrian in inspired form.
The Spanish goalkeeper continued to frustrate the Foxes during extra-time before King finally beat him with 116 minutes on the clock.
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Leicester started well when Marc Albrighton threaded a lovely pass down the left side of the box for Leonardo Ulloa, but his shot was blocked at the near post by Adrian.
The Foxes were soon in front, though. Pedro Obiang's clearance struck Andrej Kramaric and the ball dropped to Dodoo, who calmly steered it into the bottom corner of the net with his right foot from 15 yards out.
West Ham did eventually settle and Victor Moses sent a shot into the side-netting before James Tomkins' glancing header from a Manuel Lanzini free-kick skidded wide.
Kramaric's lung-bursting run from inside his own half deserved a better finish from the Croatian who, after getting between the two West Ham centre-backs to be one-on-one with the goalkeeper but making a mess of his audacious lobbed finish.
The visitors' first real piece of good build-up play resulted in the equalising goal. Obiang, Aaron Cresswell and Zarate were involved in a move from right to left before Zarate beat Mark Schwarzer with a 25-yard shot that deflected off Leicester defender Marcin Wasilewski.
Dodoo almost restored his side's lead in first-half injury time, but stretching at the far post to reach Albrighton's cross from the right he could only poke the ball into the side-netting.
Adrian came to the fore in the second half. First he repelled a long-range effort from Albrighton and then pushed away an Ulloa header.
King then had a diving header cleared off the line after a long throw-in caused confusion inside the West Ham box.
Christian Fuchs nearly caught out Adrian from a free-kick midway through the second half. The defender shaped to cross the ball but whipped in a curling left-foot shot that had Adrian scurrying across his goal to push behind.
Yohan Benalouane was the next man to be thwarted by Adrian as extra-time loomed.
Adrian then came out on top in one-on-one situations against Jeff Schlupp and Riyad Mahrez in the first period of extra-time before quickly getting down to push away another Schlupp effort during the second period of 15 minutes.
However, his resistance was eventually broken by King with four minutes remaining, prompting his manager Claudio Ranieri to conduct the home crowd's cheers and encourage them to make more noise from his position in the technical area.