The Spaniard swept home Juan Cuadrado's cross to finally break the deadlock in a poor game at the Stadio Olimpico, as the Bianconeri toiled in the absence of some key players.
Alvaro Morata came off the bench in extra time to score the winning goal as Juventus saw off AC Milan in a disappointing Coppa Italia final to secure a second consecutive domestic double.
There was no splitting the sides during regulation time at the Stadio Olimpico but substitute Morata broke Milan hearts in the 110th minute with the crucial strike.
Victory means Juve enter the record books as the first team to complete a Serie A and Coppa Italia double in back-to-back seasons.
It could so easily have been a different story for a Milan side that created the better chances during the initial 90 minutes, with Giacomo Bonaventura and Andrea Poli missing their best opportunities.
Their profligacy was punished when Morata swept home Juan Cuadrado's cross deep into extra time within two minutes of being brought on to secure another major honour for ex-Milan boss Massimiliano Allegri.
Milan, who had late penalty appeals turned down, now miss out on European football for a third consecutive season, with Sassuolo qualifying for the Europa League.
Head coach Cristian Brocchi - who replaced Sinisa Mihajlovic in April - will now wait to learn his fate amid rumours of a takeover by a Chinese consortium.
Brocchi, a victor with Milan the last time they won the cup in 2003, would have been happy with Milan's aggressive start but Juve were unlucky not to be awarded a penalty when Paul Pogba was clipped by Davide Calabria in the area.
Calabria was involved at the other end in the 13th minute when his teasing cross was prodded just wide of the right-hand post by Bonaventura.
Bonaventura again troubled the Juventus defence by cutting in from the left and angling a low strike that was deflected to force Neto into a smart reaction save with the ball squirming towards goal.
Allegri's men were handed a huge reprieve when Juraj Kucka picked up a wayward pass in the middle and launched a lightning counter-attack that ended with Poli wastefully side-footing over from Keisuke Honda's cut-back.
Milan were lacking a clincal finish again shortly after the restart when Kucka dragged a shot wide when unmarked 20 yards from goal.
That failure to score was almost punished in the 69th minute when Pogba found space in the area but teenager Gianluigi Donnarumma reacted brilliantly to a big deflection to save.
Milan pushed back in the closing stages but a goal was not forthcoming and the match headed for extra time.
Juve had the first opportunity of the additional two periods, with Pogba bringing the best out of Donnarumma with a 25-yard drive, while Carlos Bacca saw an acrobatic effort go narrowly over the crossbar.
But with the clock winding down Juve grabbed a dramatic winner. Cuadrado centred from the right and Morata - who has been linked with a close-season exit - swept home first time.
Milan's calls for offside went unheard and they were further aggrieved when Honda went down only to see his penalty appeals against Giorgio Chiellini waved away.
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