Rubin's Gokdeniz Karadeniz scored after six minutes and Pablo Orbaiz struck deep into added time to give the Russians, who played the entire second half with 10 men after Roman Sharonov was sent off, a shock 2-0 win at Atletico.
Anzhi beat Hannover 3-1 and Zenit won 2-0 at home against five-times European Cup winners Liverpool while goals from Vladimir Darida, Frantisek Rajtoral and Stanislav Tecl helped unfancied Czechs Viktoria Plzen upset Napoli 3-0 away.
Brazilian Oscar spared European champions Chelsea's blushes late on at Sparta Prague in a 1-0 victory and Gareth Bale continued his remarkable scoring form with two superb free kicks in Tottenham Hotspur's 2-1 home win over Olympique Lyon.
Hosts Inter Milan, three times European champions, beat Champions League dropouts CFR Cluj 2-0 with two goals from substitute Rodrigo Palacio.
The win was soured by injury-prone forward Diego Milito lasting six minutes and crying as he left the pitch with a knee problem but fellow Argentine Palacio took his place with aplomb.
Atletico grew increasingly frustrated in the second half against Kazan and leading scorer Radamel Falcao hit the woodwork as the clock ticked on.
Allowing goalkeeper Sergio Asenjo forward for a last-minute corner could prove fatal for next Thursday's second leg as Spaniard Orbaiz gleefully slotted into the unguarded net with the home side's shotstopper at the wrong end of the pitch.
"Those who don't take risks rarely win," Atletico coach Diego Simeone said after Rubin handed the Spaniards, second in La Liga, a first home defeat of the season while also ending their 12-match home winning streak in Europe.
"In the last play of the match, when we were looking for the draw, we took a risk and it didn't work out this time."
Samuel Eto'o, four-times African player of the year who has won the Champions League three times with Barcelona and Inter, was on target and missed a penalty in big-spending Anzhi's win at home to Hannover, a result which impressed coach Guus Hiddink.
"We played a good match considering we're only in the third week of preparation [for the restart of the Russian league season] while our opponents have their season in full swing," Hiddink told Russian television NTV Plus.
Hulk's unstoppable swerving effort from 30 metres broke the deadlock for Zenit after 69 minutes and Sergei Semak poked home three minutes later to break Liverpool's resistance after the English club's striker Luis Suarez had spurned several chances.
"If we can get [the next goal in next week's home leg], it can create momentum for us. There's no way the tie is over," Liverpool manager Brendan Rodgers told the club's website.
Napoli may feel slightly differently after they squandered numerous chances and were hit on the counter attack by their plucky Czech opponents.
DISTORTED NIGHT
Darida was on
