The Bianconeri move seven points clear at the summit with Napoli playing on Monday, and defeat leaves Siena five points clear of safety.
The Swiss defender gave Antonio Conte's side the lead in after 30 minutes following a perfectly weighted pass by Mirko Vicinic, before his Italian teammate 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 domination count as Lichtsteiner and Mirko Vucinic linked up excellently on the right before the former fired an effort over the Siena goal.
Claudio Marchiso then forced a superb diving stop from Gianluca Pegolo having combined with Vucinic as Juventus began to exert itself before Giovinco forced the Siena goalkeeper into a smart save at his near post.
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 and 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 Pogba in the middle of the park. His effort was tame and trickled straight through to Pegolo, though.
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 in the far corner, with Pegolo well beaten before Pogba lashed over from distance as Juventus looked to wrap up all three points.
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 18-yard box before firing into the roof of the leaving Pegolo with no chance.
The goal sprung the visitors into life and moments after the goal, Gianluigi Buffon was called into action, as he tipped Innocent Emeghara's goalbound 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.
Any chance of a comeback was dealt a final blow in the dying moments, though, as Pogba added Juve's third from the egde of the Siena area.
Substitute Emanuele Giaccherini came perilously close to adding a fourth in added time, but the three-goal victory saw Juventus extend its lead at the summit of Serie A, with Napoli able to cut the deficit back to four points when it plays Udinese on Monday.