Leicester - who were beaten 4-0 by Paris St Germain in the same competition in Los Angeles last weekend - appeared to be heading for an embarrassing defeat after Munir El Haddadi (2) and Luis Suarez scored before the break.
But Nigerian striker Musa, Leicester's record signing at a reported £16million from CSKA Moscow last month, scored twice as a second-half substitute before teenager Rafael Mujica secured Barcelona's victory late on.
Fed by fellow substitute Shinji Okazaki, Musa announced his arrival within two minutes of his introduction when he outstripped three Barcelona defenders from the halfway line and kept his composure to finish.
Musa struck again after 66 minutes when Jeffrey Schlupp won possession high up the pitch and the 23-year-old drilled his shot high into the Barcelona net.
Leicester had strong claims for a penalty when Musa tumbled under Javier Mascherano's challenge but their hopes of a morale-boosting draw were ended when Mujica struck six minutes from time.
Foxes boss Claudio Ranieri named both Jamie Vardy and Riyad Mahrez in his starting line-up just four days ahead of the FA Community Shield meeting with Manchester United at Wembley.
But the Leicester defence were almost cut open at will with Barcelona pair Lionel Messi and Suarez too hot to handle.
Demarai Gray should have given Leicester a fourth-minute lead from Danny Drinkwater's brilliant pass, but Barcelona's slick approach play was eventually rewarded after 26 minutes.
Messi caught out Danny Simpson with a clever ball inside the full-back and Munir's excellent left-foot finish did the rest.
Suarez doubled the lead eight minutes later after he evaded Robert Huth and Ben Chilwell in a tight area and poked home past Ron-Robert Zieler.
Huth and Andy King had chances to reduce the deficit and Leicester were punished on the stroke of half-time when Munir sprinted on to Suarez's inch-perfect pass and finished nonchalantly
Source : PA
Source: PA