The Swiss defender gave Antonio Conte's side the lead after 30 minutes, following a perfectly weighted pass by Mirko Vicinic. His Italian team-mate then secured all three points in the 70th minute, only for Pogba to add a third late on.
Andrea Pirlo forced out the first real opportunity of the encounter after Giovinco was fouled on the edge of the Siena box, but the Juventus midfielder could only guide his free kick over the bar.
The hosts enjoyed the larger share of possession in the initial 15 minutes, and looked to make their dominance count, as Lichtsteiner and Mirko Vucinic linked up excellently, before the former fired an effort over the Siena goal.
Claudio Marchiso then forced a superb diving stop from Gianluca Pegolo having combined well with Vucinic as Juventus began to exert themselves. Giovinco followed up by working the Siena goalkeeper again, but the shot-stopper was equal to it.
The Bianconeri deservedly took the initiative with a half hour gone after Pegolo palmed Vucinic's lofted pass onto the shins of the surging Lichtsteiner, who bundled the ball into the far right corner.
Juventus looked to add a second, moments later, following some good work by the creative Vucinic and Kwadwo Asamosh before the latter picked out Paul Pogba in the middle of the park. However, his effort was tame and trickled straight through to Pegolo.
Pirlo came close to doubling the hosts' advantage on the hour mark, but couldn't direct his audacious chip from the edge of the 18-yard box into the far corner.
With 15 minutes remaining the Turin outfit secured the win after Giovinco was picked out by Pirlo from a free kick. The former pushed down the left side of the Siena box before firing into the roof of the net leaving Pegolo with no chance.
The strike sprung the visitors into life and moments after the goal, Gianluigi Buffon was called into action, but tipped Innocent Emeghara's goal-bound header onto the bar.
Christian Terlizzi came even closer for Siena in the final five minutes, beating Buffon from the edge of the box, only to see his effort cannon back off the foot of the post.
However, any chance of a comeback was dealt a final blow in the dying embers, as Pogba added a third from the edge of the Siena area.