The Blues took an early lead through Fernando Torres and looked likely to finish off the game with ease, but they made it difficult for themselves in the second half.
The Premier League outfit conceded three preventable goals, with one being gifted to the home side by the referee, who awarded an unjust penalty.
Sports Mole looks over the clash that ensured a final-four place for last season's Champions League winners.
On target 10
On target 5
Was the result fair?
In terms of the aggregate scoreline, the result was a fair reflection of the two legs. An assured start from Chelsea, who led 3-1 ahead of tonight's encounter, resulted in an early goal through Fernando Torres on the night in Moscow, but a slight wobble in the second half allowed Rubin to find their feet. The home side controlled the match after the break, but they ran out of time to get the two vital goals they needed.
Rubin Kazan's performance
The home side failed to make an impact in the final third during the first half, despite having the majority of possession. It wasn't until the second 45 minutes that they began to knock on the door. However, their first two goals could have easily been prevented if it wasn't for some poor defending by Chelsea. The third goal was converted by Bebars Natcho via the penalty spot, but the penalty should never have been awarded.
From the start of the encounter, the Blues looked comfortable and in control. An early goal by Torres allowed the visiting side to sit back and maintain their aggregate lead. While they managed to net a second goal by Victor Moses after the break following a reply from Rubin, they suffered a scare by conceding two more and giving the home side a shred of hope. Defensive frailties summed up Chelsea's second-half performance, but it wasn't enough to make them crumble completely.
Sports Mole's man of the match
Gokdeniz Karadeniz: He may have been on the losing side, but the Rubin captain took full control of the second half and found the back of the net himself to give his side some hope of qualifying. While his first touch let him down on occasion, Gokdeniz was involved in almost every attack from the home side.
It was an early and costly mistake from Rubin goalkeeper Sergei Ryzhikov, which gave Chelsea a 1-0 lead on the night. Fernando Torres received a perfect pass from Frank Lampard, which, for some reason, prompted Ryzhikov to come out from his line to go one-on-one with the Spaniard. His decision was always going to let him down as Torres lobed the ball over his head to find the back of the net.
Turkish match official Firat Aydinus had a relatively quiet game until the second half when he awarded a penalty, which should never have stood. Cesar Azpilicueta was penalised for appearing to push Aleksandr Ryazantsev in the back in the penalty area, but replays showed that the Rubin player made a meal of it.
Rubin: It's the end of Rubin's Europa League campaign, so they will switch their attention to a home clash against Rostov.
Chelsea: The Blues will learn their Europa League semi-final opponents tomorrow, while an FA Cup semi-final against Manchester City awaits them on Sunday.