Filip Kostic, who replaced injured Kenan Yildiz on the left wing, scored in the second minute with Andrea Cambiaso doubling Juve's tally after the turnaround. Veteran Jamie Vardy reduced the deficit, but it was the visitors who netted maximum points.
Serbian star Kostic only made his first start of the season in the 3-1 home success over Udinese under interim manager Massimo Brambilla, and swiftly repaid the faith of new head coach Luciano Spalletti at Stadio Giovanni Zini on Saturday night.
When the line-up was announced, it appeared that Kostic would play upfront alongside Lois Openda and Dusan Vlahovic. After he slotted past keeper Emil Audero the anticipated 4-3-3 tactics that reaped rich rewards for Spalletti at Napoli transformed into a familar 3-4-2-1 formation.
Three at the back and a lone striker had not worked for Tudor during his seven months at Juventus, his one-dimensional tactics became too predictable for opponents. When Spalletti played just a single attacker as Italy manager, they too stuttered and he left that prestigious role in June.
It was a shock to see Spalletti revert to the same tactical approach as Tudor, especially as Brambilla's side won comfortably with Manuel Locatelli as a sweeper and two attackers.
Juve skipper Locatelli, who had played for the Azzurri under Spalletti before their spat, got the nod to lead the team. As Lloyd Kelly was sidelined with a back injury, Teun Koopmeiners was a surprise alternative at left-back.
Cremonese, who came into the contest on an unbeaten run of three league games, were stung by Kostic's quick run into the centre of the box and finding the bottom right corner.
It took until 15 minutes before the hosts worried Juventus. Tommaso Barbieri picked out former England star Vardy, but the 38-year-old's piledriver went wide of the gaping goalmouth.
Vlahovic wasted scoring opportunities
Midway through the opening half Locatelli thread the ball to Vlahovic, who turned his marker and with a spellbinding dribble created space only to unleash his effort straight at the shotstopper from a tight angle.
Juventus were in cruise control, pushed back their hosts and looking likely to double their tally before the half-time whistle. Only for Audero to be equal to shots from Locatelli and Vlahovic.
The visitors found themselves under the cosh after the turnaround, absorbing the pressure and only counterattacking. Just before the hour-mark keeper Michele Di Gregorio had to save Federico Bonazzoli's shot from finding the top left corner.
Sensing that Cremonese were aiming to continue to control the second half, Spalletti swapped toothless Openda for Francisco Conceicao and swiftly paid dividends with Cambiaso quickest to a rebound off the crossbar to double their lead.
Spalletti tried his luck
Spalletti tried another roll of the dice by sending on 19-year-old Vasilije Adzic and Joao Mario for Kostic and Khephren Thuram with just over 10 minutes remaining.
Sure enough, following the Juventus changes, there was another goal. Although this time it the hosts who netted on 83 minutes. A fast break saw Dennis Johnsen pick out Vardy with a superb aerial pass, who made no mistake to beat the defense and Di Gregorio.
This strike jolted Spalletti to make further changes, Weston McKennie and Vlahovic hauled off with defender Daniele Rugani and goal poacher Jonathan David given a five-minute run out plus stoppage time to work their magic.
Cremonese fluffed their chance to snatch a last-gasp equalizer when Johnsen's ambitious long-range effort whistled past the left upright.
It was a game of two halves, with Spalletti witnessing Vlahovic wasting scoring chances and learning about his other charges following only one training session and a hard-fought victory.
Spalletti is a versatile coach, who sets up his sides to win matches. He makes his bow as Juve boss in midweek at Turin's Allianz Stadium, when Sporting Lisbon are their Champions League opponents and many home supporters will be hoping that the Bianconeri can keep a rare clean sheet.
JUVENTUS: Di Gregorio - Koopmeiners, Gatti, Kalulu - Kostic (Mario, 79), Thuram (Adzic, 79), Locatelli, Cambiasco - Openda (Conceicao, 64), McKennie (Rugani, 85) - Vlahovic (David, 85). Subs: Perin, Zhegrova, Miretti, Rouhi, Scagia, Felipe