The winger got on the end of Ahmed El Mohamady's superb cross from the right and sent a fine volley across goal and into the right corner.
It gave Villa a 3-2 aggregate triumph and left Leicester distraught, with the match having looked destined to go to extra-time.
Matt Targett had given Villa a 12th-minute lead, but Leicester deservedly levelled through Kelechi Iheanacho, who also scored in the first leg, in the 72nd minute.
But Villa was not to be denied, and the home fans poured on to the pitch to celebrate an upcoming trip to Wembley for the final, which will be played against either Manchester City or Manchester United.
🙌🏻 @AVFCOfficial fans have gone crazy, lifting matchwinner @Trezeguet to the skies!!! What a finale!!— beIN SPORTS (@beINSPORTS_AUS) January 28, 2020
⏱ #CarabaoCup SF2 FULL-TIME: @AVFCOfficial 2️⃣-1️⃣ @LCFC (Villa wins 3-2 on aggregate)
Watch LIVE on beIN SPORTS CONNECT ▶️ https://t.co/3lXaI3OgGR#EFL | #AVLLEI pic.twitter.com/VFPjOUQOM7
Those two rivals will play the second leg of their semi-final at Etihad Stadium on Thursday (AEDT), with City leading 3-1 on aggregate after the first leg.