Higuain, who has been dropped from the Argentina squad, was left out of Juve's starting lineup for the second successive match. But he was brought on for Juan Cuadrado on the hour mark and responded by scoring nine minutes later and then helping to line up his team's second goal.
Mario Mandzukic netted Juve's second as the Italian side moved onto three points in Group D, three below Barcelona, which won 1-0 at Sporting Lisbon.
"I congratulate him and we are very happy, because we needed him and his goals."
It was new coach Takis Lemonis's first match in his fourth spell in charge of Olympiakos after replacing Besnik Hasi two days previously.
Juventus, last season's finalist, was looking for its first points in the competition after losing 3-0 at Barcelona in the opening round. But it was forced into a late change when Miralem Pjanic pulled up in the warm-up and was replaced by Rodrigo Bentancur.
Cuadrado's cross was headed goalward by Mandzukic but Silvio Proto finger-tipped the ball over the bar and then punched away Stefano Sturaro's header from the resulting corner.
Proto also denied Mandzukic again and Paulo Dybala before Olympiakos almost scored an own-goal on the stroke of halftime when Alex Sandro's cross was turned onto the post by Bjorn Engels.
The visitors looked threatening on the counterattack, but the match changed when Higuain was brought on. The former Napoli and Real Madrid forward broke the deadlock in the 69th minute, firing in the rebound after his initial volley from Sandro's cross was blocked.
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