The Chilean slotted home from the penalty spot in the 8th minute, his first league goal since November, when he scored in a 6-1 win against Pescara.
He then doubled the lead 20 minutes later, rifling home from close range.
As a result, Juventus are now 11 points clear of Napoli at the summit of Serie A with only six matches remaining.
Napoli could only draw 1-1 with third placed AC Milan on Sunday, leaving Antonio Conte's men with the Scudetto well within their sights.
Lazio, on the other hand, despite losing seven of their last 11 league matches, remain in fifth position level on 51 points with city rivals Roma, though ahead thanks to a better head-to-head record.
The home side started impressively with Brazilian Hernanes forcing Juventus goalkeeper Gianluigi Buffon into a good save as he managed to squeeze his 20 yard shot through a sea of players.
That momentum didn't last long, as Mirko Vucinic weaved his way towards goal Lorik Cana clumsily tripped the Montenegrin giving the referee no choice but to point to the penalty spot.
Vidal dispatched the spot-kick with ease into the bottom right corner sending Federico Marchetti the wrong way in the process.
Lazio could have clawed themselves back into the match when Ogenyi Onazi was played in on goal by Miroslav Klose, but the young Nigerian ballooned his shot high and wide.
That miss was a crucial one as it wasn't long before Vidal had his second.
Cana was once again culpable as he deflected a Claudio Marchisio ball into the path of Vidal who smashed past a helpless Marchetti.
In the second period Lazio once more came out with more intent. This time, a Ciani header forced Buffon into a full stretch save low to his right.
Andrea Pirlo beautifully bent a 25-yard free kick up and over the wall but Marchetti was equal to it, though, he parried into the path of an onrushing Marchisio who could only fire over the bar when it seemed easier to score.
Second half substitutes Ederson and Libor Kozak combined well and should have halved Juventus' lead. The Brazilian's inch prefect cross was somehow headed wide with the goal gaping and Buffon rooted to the spot.
Lazio were knocking on the Bianconeri door as Onazi's 25-yard pile driver was just off target.
Kozak had one final opportunity at the death, but directed a low cross from the left wide. Klose also fired just past the right post with the last kick of the match.
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