They surpassed the previous record of 263-5, set by Royal Challengers Bangalore in 2013
Juventus defender Giorgio Chiellini lost possession in his own half and Florenzi finished off a quick exchange of passes by gently chipping the ball over Wojciech Szczesny in the 79th minute. Dzeko then finished off a counter-attack in stoppage time.
Juventus wore their controversial new strip for the first time with black-and-white halved shirts replacing the traditional stripes.
Both teams hit the woodwork in the first half and Cristiano Ronaldo had a 63rd minute goal ruled out after he was caught fractionally offside when he collected Paulo Dybala's pass before running on to slot the ball past Antonio Mirante.