Cuadrado netted the only goal in the 76th minute, seven minutes after replacing Paulo Dybala as Juve were down to 10 men following Mario Lemina's sending-off nine minutes into the second half.
Italy keeper Buffon, who made a rare gaffe in the 1-1 World Cup qualifier draw against Spain earlier this month, saved Alexandre Lacazette's 35th-minute penalty and made a couple of decisive saves before Cuadrado struck the winner.
Massimiliano Allegri's team retained the lead in the group with seven points from three games, ahead of Sevilla, who beat Dinamo Zagreb 1-0, on goal difference. Lyon are third on three points with Dinamo in last place after three defeats from as many matches.
Juventus, who had won their last five games conceding only one goal but were without the injured Mario Mandzukic and Giorgio Chiellini, dominated early on as Lyon struggled to keep the rhythm in the midfield.
Gonzalo Higuain was denied by Anthony Lopes in the 24th minute but it was Lyon who had the best opportunity of the first half.
The hosts were awarded a penalty after Leonardo Bonucci brought down Mouctar Diakhaby in the box, but Buffon tipped away Lacazette's weak attempt from the spot.
Lopes dived onto his left three minutes before the break to deny Higuain's powerful header as Juve continued to push.
OL, however, still had another great chance five minutes into the second half but Buffon superbly parried Nabil Fekir's shot with his right hand at the end of a sharp counter attack.
The game was then Lyon's to lose when Lemina picked up a second yellow card for a foul on Fekir and was sent back to the dressing room.
Buffon was at it again in the 71st minute with a sensational save to deny Corentin Tolisso's downward header from point-blank range.
Lacazette, who made his comeback from injury last weekend, was substituted by Maxwel Cornet in the 72nd but his replacement had no impact.
Juve's substitution of Dybala by Cuadrado was more inspired as the Colombia midfielder scored with a powerful shot into the opposite side of the net from the right side of the box.
(Writing by Julien Pretot; Editing by Pritha Sarkar)
