"I made a choice," Juventus coach Massimiliano Allegri told Italian television. "Higuain was in less good shape compared to the others, but he is already moving quicker.
"He has never been a problem and never will be. He's a player that can make a difference and win us games," he added.
Juventus had spent the first hour of Wednesday's clash looking dominant but not threatening, but that would all change with the introduction of Higuain.
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With his instinctive positioning, crosses into the box that previously looked aimless became dangerous, and he also freed up space for strike partner Mario Mandzukic, who netted the second goal in the 80th minute.
Juventus have now won all five home games in all competitions this season and have yet to concede a goal to a visiting team.
Juve captain Gianluigi Buffon also praised Higuain for his effort.
"People will say the credit should go to Allegri or his team mates, but the credit goes to him (Higuain), because in such moments the only one that can give the answer is the one directly concerned," Buffon said.
"I congratulate him and we are very happy, we needed him and his goals."
No other side has managed to keep Juventus scoreless at home this season for as long as Olympiakos did, but it was little consolation to the Greeks.
Olympiakos are bottom of group D after two defeats with Juventus in third behind Sporting Lisbon on goal difference after the Portuguese side lost 1-0 at home to leaders Barcelona.
"We leave the pitch with the feeling that we gave everything against a better team," Olympiakos goalkeeper Silvio Proto told reporters.
"In the Greek league we are always favourites, in the Champions League we have to defend against Juventus or Barcelona and take our chances," added the keeper, who pulled off a string of fine saves until Higuain broke the deadlock.
"We are in a tough group, (but) we can get points if we believe in ourselves. We are a young side and we must make the most of this international experience."
(Reporting by Philip O'Connor; editing by Rex Gowar)
