Two goals from Ciro Immobile, including an opening penalty, had seemingly set Lazio on the way to a comfortable win. But Paulo Dybala netted a stunning free kick in the 85th minute and converted a penalty in the first minute of stoppage time.
The match appeared to be heading for extra time before substitute Murgia, who had come on as an 80th-minute substitute, scored the winner in dramatic fashion.
The Italian Super Cup normally pits the league champion against the cup winner, but Juventus had again won the double last season – for the third successive year. But the result does go some way to avenging Lazio’s defeat to Juventus in the Italian Cup final in May.
Shortly after that success, Juventus lost a second Champions League final in three seasons, while reports of training ground bust-ups and the departure of key defender Leonardo Bonucci to Serie A rival AC Milan has made it a difficult off-season for the six-time defending Italian champions.
Juventus were looking to get back on track in Rome, in the traditional curtain-raiser, and they started strongly. Lazio goalkeeper Thomas Strakosha pulled off a great save early on to
keep out Juan Cuadrado’s effort from close range and denied Gonzalo Higuain moments later in a frantic opening five minutes.
Lazio withstood the pressure and slowly took control of the match before going in front shortly after the half-hour mark. Immobile was brought down by Juventus goalkeeper and captain Gianluigi Buffon, who received a yellow for his troubles, and he dusted himself down to fire the resulting penalty into the bottom right corner.
Lazio almost doubled their lead minutes later but Buffon pulled off a double save to deny first Dusan Basta and then former Liverpool man Lucas Leiva.
Lazio did extend its advantage nine minutes into the second half when Marco Parolo whipped in a cross and Immobile sent a looping header into the far corner.
Juventus coach Massimiliano Allegri immediately reacted, bringing on new signings Douglas Costa and Mattia De Sciglio and later also introduced Federico Bernardeschi.
That had an effect and Dybala got Juventus back into the match when he curled a free kick into the left side of the goal.
Juventus was then given the chance to level when it was awarded a penalty after Adam Marusic tripped Alex Sandro. Dybala had missed the decisive penalty in the shootout in last year’s Super Cup defeat to Milan but he stepped up and converted.
Another twist was still to come. Three minutes later, Jordan Lukaku went on a winding run before pulling back from the byline for Murgia, who turned 21 on Wednesday, to smash in the winner.