The Spaniards were the pre-match favourites but the visitors stunned their opponents by taking a first-half lead through Gokdeniz Karadeniz.
Rubin had to play through the second half with ten men after captain Roman Sharonov was given his marching orders for a second yellow-card offence right before the break.
However, the Russians snatched a second goal deep into second-half stoppage time through Pablo Orbaiz to claim two vital away goals.
Find out how all the action unfolded with our minute-by-minute text commentary below.
7.12pmGood evening and welcome to our live text coverage of this Europa League last-32 clash at the Vicente Calderon. There's just under an hour until kickoff but we'll have team news and build-up for you until then.
7.15pmWe're in for an interesting game tonight. Atletico are the red-hot favourites considering they are defending champions and have home advantage but Russian teams are no pushovers, as Liverpool and Hannover 96 found out earlier today.
7.19pmHaving said that, the omens are very much in Atletico's favour. They haven't lost a single game at home all season and Rubin have not played a competitive match since December due to the winter break they have over in Russia.
7.25pmDiego Simeone's side did lose on the road to city rivals Rayo Vallecano in their last outing, though, and the Argentine has indicated that he could see some changes to his starting XI tonight. Some quotes from him coming up...
7.29pm"The team have been responding well to the physical demands, but we have struggled to play well away from home. Now we have a lot of games in a short space of time and we have to have everyone available. We have to choose our rotations wisely so we can be competitive in all three competitions."
7.34pmOf course, Rubin famously defeated Barcelona in the Champions League at the Camp Nou three seasons ago, a fact Simeone is only too aware of.
7.36pm"I don't think Barcelona dismiss any team lightly and we respect Rubin and know of their potential. We'll have to play with all the intensity that a competition like the Europa League demands."
7.47pmThe Rubin defence will no doubt have their hands full dealing with both Adrian Lopez and Radamel Falcao this evening. A pairing like that is every defender's nightmare. I'm going to go out on a limb and say those two will fire Atletico to victory tonight.
7.55pmThere are a few former La Liga players among the Russian side's ranks this evening - ex-Athletic Bilbao midfielder Pablo Orbaiz, former Malaga forward Salomon Rondon and former Villarreal defender Ivan Marcano.
8.00pmThe two teams are out on the pitch now and the action is about to commence. A lot of empty seats around the Vicente Calderon this evening, which is somewhat disappointing to see.
0 minWe are under way here. Atletico in their iconic red and white stripes shoot from right to left while Rubin are in all green.
2 minA confident start from the home side. They try to hoist the ball forward early on but Mario Suarez loses possession. Rubin claim possession inside their own half.
4 minJuanfran and Tiago exchange passes along the right but the latter's cross is claimed by Sergei Ryzhikov between the Rubin sticks without too much difficulty.
6 minGOAL! Atletico Madrid 0-1 Rubin Kazan (Karadeniz)
7 minWe have a breakthrough and who'd have predicted this? Jose Salomon Rondon found space after giving his marker the slip and shot at goal but was denied by Sergio Asenjo. The rebound fell kindly for Karadeniz, who was on hand to claim his third goal of the competition.
9 minRondon goes on the attack again but is dispossessed by Diego Godín wide on the left. The Russians certainly don't look like a team who have not played a competitive game since last December.
11 minJuanfran tumbles the in box but does not appeal for a penalty. However, he does win a corner for his efforts which is nodded out for a goal kick by Juanfran.
14 minCristian Rodriguez goes on a mazy run along the left flak but is snapped in full flight by Roman Sharonov, who is booked for the challenge. Atletico win another corner from the resultant set piece.
16 minSHOT! The Rubin defence clears a cross only as far as Rodriguez, who shoots from the edge of the box but puts his effort into the stand. I think Ryzhikov would have been all over that had it been on target.
18 minGood play from Bebars Natcho in the centre of the park there. He exchanges passes with Eremenko and keeps possession well, running rings around the Atletico midfield.
19 minAtletico have not lost at home in Europe in their last 12, so this would be quite a shock if things remain as they are. Rubin have been very organised thus far and are looking good for that lead.
22 minSHOT! The Rubin back line gives Falcao far too much space around their area and he shoots wide from 20 yards. You don't give prolific forwards like him that kind of freedom. Errors like that could be the Russians' undoing.
26 minPablo Orbaiz handballs, gifting a free kick to the hosts but they are unable to create anything from the set piece. The ball is now with Rubin keeper Sergei Ryzhikov for a goalkick.
28 minCristian Rodriguez makes a run down the left and is tackled by Roman Sharonov at the byline. He appeals for a corner, but I think it was he who had the last touch, the ball bouncing off his shin. Good, persistent play from him nevertheless.
31 minSHOT! Neat build-up play by the hosts is squandered as Arda Turan sends a shot well over the crossbar. Rodriguez did well to shrug off a challenge from Sharonov in the build-up. This is turning into quite a scrap between those two.
33 minThis has turned into quite an evenly-matched contest. Atletico are getting plenty of balls forward but Rubin are restricting them to long-range strikes. The Russians, on the other hand, look deadly on the counter-attack.
35 minCHANCE! Tiago plays in a dangerous ball from wide on the right, which Sharonov attempts to put behind but it defects into the hands of Ryzhikov. He was lucky not to put through his own net there. Tiago's delivery was first-rate.
37 minThere's a half-chance for Rondon at the other end as the striker latches onto a long ball, but his first touch is poor, allowing Asenjo to gather up the loose ball.
38 minSHOT! Rubin almost claim a spectacular goal through Roman Eremenko, who meets Bebars Natcho's cross with a first-time volley that crashes into the side netting. That would have been a wonderful goal!
42 minDiego Godín and Roman Eremenko jump up for the same ball and the Uruguayan defender catches his opponent in the head with an elbow. That looked painful but there was no malice there. The Atletico man is over there apologising now.
44 minFalcao has another crack at goal from long range and puts it wide. He has been uncharacteristically wasteful tonight and seems to want to shoot on sight.
45 minRED CARD! Roman Sharonov is sent off for his second bookable offence. He brought down Falcao right on the edge of the area! Rubin are now without their captain and are playing with one central defender!
45+1 minCHANCE! Atletico's best chance of the half falls to Filipe Kasmirski just before the break. The ball finds him inside the area directly from the free kick but he blazes his close-range effort over the bar. That's why he plays in defence!
45+1 minHALF-TIME: Atletico Madrid 0-1 Rubin Kazan
8.57pmSo the Russians lead the holders by one goal to nil right in their back yard through that Gokdeniz Karadeniz strike, but will have to defend that lead with just 10 men in the second period.
8.59pmRubin captain Roman Sharonov can have no complaints over his sending-off. He picked up two yellow cards for a pair of reckless challenges, putting his teammates under intense pressure for the remainder of this first-leg clash.
9.01pmIt's been a thoroughly entertaining game. Rubin have been well organised and difficult to break down at the back, leaving Atletico with no option but to pelt their goal with long-range efforts, which isn't paying off for them.
9.03pmRadamel Falcao has been off the boil by his own high standards. He has been trigger-happy all evening and put more shots than I can count into the stand. Filipe Kasmirski will no doubt have nightmares about that glaring miss of his shortly before the break.
45 minA half-time substitution for Atletico: Koke is coming on for Mario Suarez. They have brought on a winger, suggesting a change of shape for the hosts in the second period.
48 minCésar has taken on the captain's armband for Rubin, a man who knows tonigh's opponents well having graduated from Real Madrid's academy.
50 minAtletico have had a lot of possession in the early stages of this second half. One of their attacks has just ground to a halt as Karadeniz wins the ball from Rodriguez.
53 minAnother Atletico attack goes begging as Adrian attempts to latch onto a long ball but he can't muster the pace to reach it. I expect we'll see plenty of possession from the hosts in this second period as they look to make that numerical advantage count.
56 minThe home side win a corner as Filipe Kasmirski's cross cannons off a green short and goes behind but they squander the resultant set piece.
58 minWe're approaching the hour mark and neither side has created any goalscoring opportunities in this second half. Rubin appear to have adopted a 10-0-0 formation to keep the Spaniards out!
60 minAtletico make a change on the hour mark: Daniel Alberto Diaz is off and Raul Garcia comes on. An attack-minded sub by the hosts with a midfielder replacing a defender.
62 minHalf-chance for the home side as Garcia's first contribution is to hit one wide from inside the box. He did well to latch onto the loose ball but couldn't direct his effort on target.
64 minBOOKING! Sergei Ryzhikov is shown the yellow card from time wasting. He was taking an age with that goal kick and was fully deserving of that caution.
66 minAnother attacking substitution for Atletico: Saul Níguez Esclapez comes on for Filipe Kasmirski. He deserved to be subbed after missing that sitter in first-half stoppage time!
68 minRubin have been non-existent going forward in this second period. It's a shame they were reduced to ten men as it's tipped the balance of what was an evenly-matched contest. However, Atletico have not created much in the way of clear-cut chances despite all of their possession.
71 minFalcao is trigger-happy on the edge of the area once again. He tries his luck when he had teammates in space, shooting directly at Ryzhikov, who gathers the ball easily.
73 minCHANCE! Arda Turan goes for goal from outside the box and his effort takes a wicked deflection on its way in, almost catching out Ryzhikov, who saves with his legs. The Russian shot-stopper tips a Rodriguez effort over the bar moments later!
78 minOFF THE BAR! Falcao picks up the ball in the area and shoots on the turn, beating Ryzhikov but not the crossbar! That's as close as Atletico have come all evening!
81 minWHAT A MISS! Atletico win a corner through Godín and Adrian is presented with an open goal from the resulting cross but somehow heads wide! That one will haunt him for some time!
85 minRubin make their first change, bringing on Vladimir Dyadyun for Rondon, who looks knackered. It's a like-for-like swap up front for the Russians.
88 minIt's another substitution for the visitors, with their goalscorer Karadeniz making way for defender Oleg Kuzmin. Rubin are playing with five at the back now as they attempt to see this one out.
90 minThere will be four minutes of stoppage time to be played. Can Rubin hang on and make it a trio of Russian victories in this competition tonight? I'm certainly not betting against them at this stage.
90+2 minANOTHER GLARING MISS! The ball penetrates a sea of green shirts and falls for Cristian Rodriguez at the back post, just yards out, but he somehow shoots wide! Unbelievable! What a let-off for the visitors.
90+5 minGOAL! Atletico Madrid 0-2 Rubin Kazan (Orbaiz)
90+5 minA stunning turn of events as Rubin snatch a second right at the death! It's the Spaniard Pablo Orbaiz who put the ball in the net and it was a real suckerpunch by the visitors. Atletico keeper Asenjo came forward for a late corner, which the visitors cleared and went straight on the break, allowing Orbaiz to put the ball into an empty net!
90+5 minFULL-TIME: Atletico Madrid 0-2 Rubin Kazan
10.00pmSimply unbelievable! Rubin Kazan leave the Spaniards with a mountain to climb after snatching that late, late goal against the run of play.
10.04pmA deserved victory for the Russians tonight. They defended tenaciously while Atletico were criminally wasteful in front of goal. This is the first home European match the hosts have lost in 12 and a result that sees Rubin become the third Russian side to claim victory at this stage in the competition.
10.05pmThat's all from me here this evening. Many thanks for joining Sports Mole for this Europa League clash in Spain.