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 in the 72nd minute.