Two goals from Paul Pogba - either side of one for Carlos Tevez - completed a routine triumph in Rome and the result means Juve have now gone 20 Serie A matches without losing against the side from the capital.
The win restored the champions' three-point lead at the top of the table, after Roma had moved level with them thanks to a 2-1 victory at Atalanta earlier in the day.
Juventus were comfortably the better side throughout and never looked like relinquishing their advantage after Pogba's composed strike gave them the edge.
Tevez's goal - his ninth in the league this season - came early in the second period as Juve assumed complete control, which was underlined when Pogba tucked home his second in the 64th minute.
There was one sour note for the visitors when Simone Padoin was shown a second yellow card for a block on Antonio Candreva 20 minutes from time, but it did little to affect the outcome as Massimiliano Allegri's side managed comfortably being a man down.
Following an uneventful opening to the game, Juve broke the deadlock midway through the half thanks to a devastating counter-attack.
Juve broke through Tevez after clearing a Lazio free-kick and his lofted pass was deftly controlled by Pogba, who slotted a cool finish beyond Federico Marchetti.
The France international almost doubled his tally in the 29th minute, but his curled effort from the left-hand corner of the box struck the outside of the post with Marchetti well beaten.
Gianluigi Buffon was tested for the first time eight minutes prior to the interval when the goalkeeper gathered Candreva's awkward bouncing free-kick at the second attempt.
Juve continued to assert their dominance after the break and doubled their advantage in the 55th minute through Tevez's well-taken strike.
Claudio Marchisio broke forward and, with Lazio exposed at the back, slipped a pass to the Argentinian, who took a touch before planting a low finish into the bottom left-hand corner.
Candreva attempted to drag his side back into the match, but once again Buffon proved equal to his rasping drive from distance.
Any hopes of an unlikely comeback were quickly dashed, however, as Pogba slotted in a low finish following a sublime reverse ball from Roberto Pereyra.
Padoin, who had been booked in the first half for handball, was then dismissed, but the visitors continued to look the more threatening.
Federico Mattiello, introduced in place of Pereyra in the wake of Padoin's sending off, brought a flying save out of Marchetti as Juve cruised to a fourth successive win in all competitions.