Lyon were heavy favourites coming into this game at the Stade de Gerland, but were left reeling early on when Vladimir Dyadyun gave Rubin the lead after volleying home from close range in the third minute.
However, the Ligue 1 giants bounced back promptly, when Michel Bastos' pinpoint ball found an unmarked Bafetimbi Gomis, who volleyed home with aplomb.
And five minutes before half-time, Lyon had taken the lead, after Gomis found space on the left and fired a speculative effort across goal, which was inadvertently turned into his own net by Saba Kvirkvelia.
Lyon continued to dominate proceedings in the second half and were rewarded for their endeavour with a third in the 71st minute.
A smart corner from Kim Kallstrom found Jimmy Briand at the near post, who flicked a sharp header off the underside of crossbar and into the back of the net before Sergei Ryzhikov.
Gokdeniz Karadeniz had two decent opportunities to net another away goal for Rubin but was thwarted on both occasions by Hugo Lloris, as Lyon held on for a well-deserved victory.