Stephan Lichtsteiner and Sebastian Giovinco gave the Bianconeri a two-goal advantage, but Siena hit the woodwork twice as they made Juve work hard for their win.
Paul Pogba then ended Siena's hopes with a third goal in the dying stages.
The three points take Antonio Conte's side further ahead of Napoli at the top of the table, while Siena remain just a point off the foot of the table and five adrift of safety.
Conte had warned that this would be one of their toughest and most important games of the season, and his message appeared to have been understood by his team.
Not for one minute did it look like they would take the Serie A strugglers lightly and a committed attacking effort led to Claudio Marchisio testing Gianluca Pegolo for the first time in the 20th minute.
Ten minutes later, Lichtsteiner somewhat fortunately gave the home side the lead.
He surged into the area to meet Mirko Vucinic's pass, but he would not have reached it had Pegolo not pushed the ball onto the Swiss full-back's shin with the rebound looping into the net.
Andrea Pirlo went close to adding a second with a free-kick as Juve continued to keep their concentration high.
Giovinco made it two with a shot from a tight angle which Pegolo pushed in off the underside of his own crossbar in the 74th minute, but the day's work was far from done.
Gianluigi Buffon did well to tip Innocent Emeghara's shot onto the bar in the 76th minute before Christian Terlizzi's shot hit the post six minutes from time.
Pogba then settled Juve's nerves in the 89th minute as he took aim from 20 yards out, beating Pegolo with a low shot into the bottom left-hand corner.