The hosts almost took the lead after just three minutes when Carlos Tevez went for goal from close range, but Samir Handanovic stopped his initial effort before recovering in time to deny the striker's rebound as well.
The Italian champions wouldn't have to wait much longer to break the deadlock, however, doing so in the 15th minute when Andrea Pirlo's sublime pass found Stephan Lichtsteiner, who nodded home into the far corner.
The Bianconeri had two chances in as many minutes at the end of the first half, but on both occasions they failed to beat Handanovic, who denied Tevez before saving Kwadwo Asamoah's strike.
Juve doubled their lead less than two minutes after the restart when Inter's poor clearance from a corner allowed Arturo Vidal to play it back into the box, where Giorgio Chiellini was waiting to fire home.
Palacio had another decent sight of goal five minutes later, but once again he wasted it, meeting a low cross from the left only to blaze his shot over the bar.
That goal would have given Inter a route back into the match, but instead Juventus secured all three points shortly afterwards with their third of the night.
Handanovic spilled Paul Pogba's effort at the feet of Vidal, who made no mistake with his finish.
The visitors pushed for a late second that would make a nervy ending for Juve, and they should have got it when Palacio was left unmarked at the back post, but once again the striker failed to make the most of the chance and nodded over.
Juventus came within inches of adding a fourth in stoppage time when Mirko Vucinic's deflected effort hit the outside of the post.