The Blues, who held a 3-1 advantage from the first leg at Stamford Bridge, twice took the lead at the Luzhniki Stadium through Fernando Torres and Victor Moses, but second-half goals from Ivan Marcano and Gokdeniz Karadeniz and a Bibras Natkho penalty 15 minutes from time handed the Russians victory on the night.
Chelsea made the brighter start to the second leg, which was moved to the Russian capital because of freezing temperatures in Rubin's home region of Tartarstan.
Torres, who scored twice in the first-leg win, continued his Europa League hot streak as he struck his 19th of the season after four minutes thanks to Frank Lampard's neat through-ball. The Spaniard's first touch saw him lift the ball over the advancing goalkeeper Sergei Ryzhikov for it to bounce once on the synthetic surface and go into the net.
The goal meant Rubin needed three to force extra-time, but it was Chelsea who almost went further in front soon after. A mistake by Oleg Kuzmin allowed Moses, who also scored in the first leg, through, but he shot tamely at Ryzhikov.
Chelsea were prepared to sit and play on the counter-attack, with Nathan Ake - making his second senior start - and Ramires effective at breaking up play as Rubin went forward. On the few occasions when the defence was breached, Rubin failed to trouble Petr Cech in goal.
Jose Rondon flashed a shot wide and a tricky run by Alan Kasaev led to a shot by Roman Eremenko, which deflected off Ake but Cech, wearing leggings to guard against the cold and artificial surface of the pitch, saved to his left.
Cech had to be alert as the first half came to a close when Bebras Natcho's lofted pass found the darting run of captain Karadeniz, whose shot was well-saved by the Chelsea goalkeeper.
Rubin equalised six minutes into the second half when Pablo Orbaiz's cross was met by Marcano, who rose above Ramires to direct a powerful header into the net. Fortunately for Chelsea their response was almost immediate.
Ramires won the ball from Orbaiz and laid it off to Lampard, who found Moses. The Nigeria international played a one-two with Ramires and curled a shot into the top corner.
Rubin would not buckle, though, and continued to press forward. Cristian Ansaldi took Cesar Azpilicueta to the byline and crossed for the late-running Karadeniz, the smallest player on the pitch, to power a header beyond Cech. Marcano then struck the outside of the post with a header from another Ansaldi cross as Rubin again demonstrated Chelsea's defensive fallibility.
Azpilicueta fouled Aleksandr Ryazantsev to grant Rubin a second penalty of the tie, which, like at Stamford Bridge, Natcho converted.
Rubin continued to forge on, with Ansaldi playing as an auxiliary left-winger. He found Rondon, who headed straight at Cech.
Time and again Chelsea had to repel Rubin attacks in the closing moments and reinforcements were called as Branislav Ivanovic was brought on for stoppage time as the Blues advanced.
|Rubin Kazan||Team Statistics||Chelsea|
|0||1st Half Goals||1|
|7||Shots on Target||4|
|7||Shots off Target||3|
|61.8||1st Half Poss.||38.2|
|64.4||2nd Half Poss.||35.6|