Massimiliano Allegri's side suffered a surprise 3-2 defeat to Sampdoria last weekend, but bounced back in style to keep the pressure on Inter and Napoli, who had both won earlier in the weekend.
Juve now travel to league leaders Napoli on Friday knowing that a win will put them just one point behind Maurizio Sarri's high-flying side at the summit of Serie A.
The Bianconeri dominated throughout and should have opened the scoring in the first half, but Blaise Matuidi squandered two golden opportunities to open his account for the club following his move from Paris Saint-Germain.
However, Mandzukic eased any nerves in the 51st minute with a fine header, as Juve equalled their own Serie A record of scoring in 43 consecutive league games.
Substitute De Sciglio then scored the first senior goal of his career with a superb strike from distance on the hour before Benatia tapped in from close-range to complete the scoring in the 71st minute.
Juventus, who handed a belated debut to Benedikt Howedes following his loan move from Schalke in August, started on the front foot and should have been ahead after four minutes.
Matuidi collected Douglas Costa's pass just inside the penalty area but, after seeing off the attentions of two Crotone defenders, he flashed his shot wide of Alex Cordaz's right post.
The well-organised visitors kept Juve at bay for the opening half hour, limiting them to shots from distance and hopeful crosses, which were comfortably dealt with by defenders Arlind Ajeti, Federico Ceccherini and Mario Sampirisi.
France international Matuidi again came close to breaking the deadlock 10 minutes before the break, heading agonisingly wide from Costa's clipped cross.
Cordaz then got down well to push away Alex Sandro's fierce drive, while Mandzukic headed just wide as Juve cranked up the pressure before the interval.
Juve's relentless approach paid off six minutes into the second half as Mandzukic scored just his third league goal of the season.
Andrea Barzagli roamed into space down the right and whipped in a cross that the Croatian expertly guided into the corner with his head, giving Cordaz no chance.
De Sciglio replaced Stephan Lichtsteiner after 56 minutes and, just four minutes later, he crashed in a stunning long-range drive with just his third touch of the ball to double Juve's advantage - his first goal in over 180 appearances for club and country.
Juve then got their third 11 minutes later when substitute Miralem Pjanic's cross was parried by Cordaz into the path of Benatia, who had the simple task of slotting home from inside the six-yard box.
