Captain Cristian Noboa netted the only goal of the game from the penalty spot in first-half injury time as Rubin, having drawn three of their opening four matches in Group D and losing the other, finally found the winning formula.
- Rubin Kazan 1-0 FC Copenhagen: As it happened
The victory not only sees the Russian side gain revenge for their 1-0 defeat to FC Copenhagen in Denmark but also means they can still reach the knockout stages of the Champions League - something that would have been impossible had they failed to win.
Rubin are now a point behind second-placed Copenhagen, who are themselves a point adrift of leaders Barcelona, who can now secure both their place in the last 16 and top spot in the group if they beat Panathinaikos later this evening.
Rubin travel to Barca in the final round of matches while Copenhagen are at home to Pana.
Danish champions Copenhagen are in phenomenal form in their domestic league, having won 14 and drawn three of their 17 matches so far to lead by 16 points, and Stale Solbakken's side looked in confident mood at the start of the clash in Kazan.
However, aside from a Cristian Bolanos volley that went over for the visitors, neither side was able to create much to trouble the respective goalkeepers in the initial stages.
Rubin had a sight of goal in the 30th minute but Sergey Kornilenko's 25-yard effort flew a foot wide of the upright.
The first period looked set to end in stalemate when Rubin were given a chance to go ahead when Copenhagen winger Jesper Gronkjaer conceded a penalty after handling Noboa's inswinging free-kick.
And Noboa ensured the opportunity was not wasted, the Ecuador international firing an unstoppable penalty past Johan Wiland and into the roof of the net.
That proved to be the match-winning strike as Copenhagen were unable to find a way back into the match in the second half - although the visitors were not without their chances.
In the 48th minute a good effort from Zdenek Pospech produced an equally good save from home goalkeeper Sergei Ryzhikov, while Copenhagen also struck the woodwork in the 75th minute through Dame Ndoye.
The Senegalese striker picked up a lay-off on the edge of the box and fired in a shot that beat Ryzhikov but smashed against the crossbar before going over.
Copenhagen would also have one great last chance to salvage a point in the 92nd minute but substitute Kenneth Zohore, having created space with a good turn in the area, saw his thumping left-footed shot blocked by Ryzhikov.