The Bianconeri pressurised Siena straight from kick off and had a couple of half chances in the first 10 minutes, but couldn't find the target.
Stephan Lichtsteiner came close with a strike from distance on 15 minutes, but his effort flew over the bar.
Mirko Vucinic caused plenty of problems for the away side's back line and almost gave his side the lead with a header on 25 minutes, but his attempt was cleared well.
Lichtsteiner then gave Juve the lead on the half-hour mark, dinking over the goalkeeper after Vucinic's fine ball in behind the defence.
Paul Pogba had a shot from distance, though it never troubled the goalkeeper, who gathered the ball with ease.
Siena began to get themselves into the game in the opening stages of the second half, although they could not create any clear chances.
Andrea Pirlo came close on 59 minutes, putting a delicate chip just wide of the post.
Sebastian Giovinco doubled Juve's lead on 74 minutes, smashing past the goalkeeper after a quick free kick.
Pogba then secured the points on 89 minutes with a fine strike to make it 3-0.