City's Bernardo Silva and Mateo Kovacic both misfired in the shootout to put Madrid in the driving seat
In an attacking move that became a familiar sight during Leicester's title-winning campaign, Vardy was picked out by a long-range ball from Danny Drinkwater from inside his own half in the 32nd minute, and made no mistake when one-on-one against Lukasz Fabianski.
Morgan added a second in the 52nd minute after reacting the fastest to slam home from close range after Swansea failed to clear their lines, before Leroy Fer pulled one back for the visitors in the 80th minute, meeting Modou Barrow's cross with a superb header.