On a night when Sporting Lisbon might have deprived them of second spot in Group D, last season’s finalists ensured there would be no slip-ups with a fourth successive clean sheet.
Juan Cuadrado settled any Italian nerves after 15 minutes and substitute Federico Bernardeschi sealed matters with a fine strike in the final moments.
In the end Sporting’s defeat in Barcelona meant that this result in Greece did not matter, but Juventus controlled the contest throughout.
Wojciech Szczesny — deputising for the injured Gianluigi Buffon — made a fine save near half-time to thwart Uros Djurdjevic and El Fardou Ben Nabouhane struck the crossbar late on for Olympiacos.
But those were rare moments of worry as Juventus came out of the blocks quickly to exercise their authority.
Mattia De Sciglio slipped in Paulo Dybala after seven minutes and the Argentine cut inside Uros Djurdjevic and onto his left foot.
Dybala’s shot looked destined for the bottom corner but Olympiacos goalkeeper Silvio Proto thrust out a strong hand to divert the ball around the post.
Olympiacos’ response was Vadis Odjidja-Ofoe’s snapshot which Szczesny needed two attempts to gather in the Juventus goal.
But Juventus were ahead when Blaise Matuidi spotted the unchecked run of Alex Sandro down the left.
Sandro drove the ball across the six-yard area and Cuadrado had the simple task of tapping home into an unguarded net for his first Champions League goal since October 2016.
Cuadrado almost had another 10 minutes later from Gonzalo Higuain’s pass but Proto was out sharply to smother.
Juventus were in cruise control as Higuain had an effort deflected wide, but that created an air of complacency which Olympiacos almost took advantage of four minutes before the break.
Dimitris Nikolaou rose unchallenged at a corner and his flick on fell to Djurdjevic, who was denied by the legs of Szczesny from point-blank range.
Olympiacos took heart from that near miss and Szczesny was called upon at the start of the second half to stop Felipe Pardo and substitute Marko Marin.
After that Juventus kept Olympiacos at arms length without creating too much danger of their own.
But Sami Khedira tested Proto with a fierce shot before Bernardeschi rifled home Juventus’ second in the final minute.