Vidal's brace had the home side 2-0 up after 26 minutes, only for Miroslav Klose to halve the deficit two minutes later.
Mirko Vucinic stretched Juve's lead four minutes into the second half, though, before Hernanes was given his marching orders for a second bookable offence just after the hour mark and Carlos Tevez completed the scoring 10 minutes from time.
The visitors had the first chance after two minutes. Antonio Candreva supplied a ball into the box which Andrea Barzagli cleared as far as Hernanes, whose low shot was saved by Gianluigi Buffon.
Vidal gave himself a sighter with a left-footed shot which flew over the bar after 10 minutes, though, and four minutes later put the hosts ahead.
Paul Pogba and Vidal exchanged some neat passes before the Chilean fired a shot low past Federico Marchetti.
Candreva had another long-range effort saved by Buffon before Juve doubled their lead after 26 minutes.
Leonardo Bonucci found Vidal with a superb raking pass and the South American was on hand to once again beat Marchetti down low.
But Lazio got themselves back in the game two minutes later as Buffon could only palm Hernanes' long-range shot into the path of Klose, who had the easiest of tap-ins.
The visitors finished the first half strongly with both Stefan Radu and Hernanes bringing saves from Buffon, but they could not beat the Italy international.
Two minutes after the break Candreva blazed over the bar from distance, but just two minutes later it was 3-1.
Bonucci was the provider again as he found Vucinic, who surged into the box and produced a clinical finish.
Vucinic was looking for a second soon after but his ambitious effort never really looked like troubling Marchetti.
Hernanes was then shown a second yellow card for deliberate handball.
Candreva once again tried his luck from distance but he never looked like beating Buffon and it was Juve who went close to extending their lead as Tevez hit the bar from the edge of the box.
The Argentina striker was not to be denied with 10 minutes remaining, though, showing great skill to beat Loris Canas and fire past Marchetti.
Lazio were still pushing and Ederson's free-kick had to be gathered on the line before Vidal fired wide from distance looking for his hat-trick in the final minute.