Paul Pogba opened the scoring in the first half shortly after replacing Claudio Marchisio but it was three goals in six second-period minutes which proved decisive.
Giorgio Chiellini, Stephan Lichtsteiner and Carlos Tevez completed the rout prior to the hour mark, ensuring the Serie A champion secured its first silverware of the new campaign.
Juventus named a strong side for the meeting with the Coppa Italia holder, although Fernando Llorente was omitted to allow Tevez to partner Mirko Vucinic in attack. Lazio, meanwhile, was without the services of captain Stefano Mauri following his six-month suspension for match-fixing offenses.
The game started at a frenetic pace, with both sides carving out presentable opportunities in the opening stages.
Only a desperate Arturo Vidal headed clearance prevented Andre Dias grabbing a goal for Lazio in the 10th minute, while Vucinic went agonizingly close to nodding an Andrea Pirlo cross into the net in the immediate aftermath.
A much-required break in play in a breathless start was provided in unfortunate circumstances in the 21st minute, when Claudio Marchisio was forced to leave the field after picking up an injury while challenging Stefan Radu for the ball.
But the unplanned introduction of his replacement Pogba led to the deadlock being broken.
Lichtsteiner worked space to receive a Pirlo ball on the right before finding the unmarked Frenchman via a deflected cross. And he made no mistake after receiving that slice of luck, turning and smashing the ball home hard and low past Federico Marchetti just two minutes after arriving on the pitch.
That goal did not bring about a let up in the intensity of the game, either, with Hernanes and Andrea Barzagli both picking up yellow cards for cynical challenges prior to a hard-fought first half coming to a close.
The end-to-end nature of the fixture continued after the break, and so it was of little surprise when Juventus' second goal came courtesy of a devastating counterattack.
Conte's side had been defending a corner in its own box but, from the clearance, Vidal found Lichtsteiner's roving run down the right and the Swiss completed the simple task of teeing up Chiellini following a lung-bursting sprint upfield.
Lichtsteiner had been a constant source of worry for Lazio throughout the match and, when Juventus grabbed a third just two minutes later, the 29-year-old was a deserving scorer. He played a delightful one-two with Vucinic to deceive the Lazio defense before producing a delightful outside-of-the-boot finish to cement Juve's utter dominance of the fixture.
But the club was not done there, as some Marchetti heroics denied Pogba but allowed Tevez to grab his first competitive goal for Juventus since joining from Manchester City from close range amid some chaotic Lazio defending.
The remaining half-hour did not see an end to the chances, but a Miroslav Klose effort that was well-saved by Gianluigi Buffon was the closest either side came as Juventus held on to seal its second-successive Supercoppa victory.