Napoli lost 3-0 at home to Czechs Viktoria Plzen. Vladimír Darida was on hand to crash the loose ball into the net after 28 minutes against Napoli, second in Serie A and featuring star forwards Edinson Cavani, Marek Hamsik and Goran Pandev.
František Rajtoral crept in unnoticed at the far post to bundle the ball past Italian international Morgan De Sanctis with 11 minutes remaining while Stanislav Tecl added a third late on to give Czech league leaders Plzen a famous victory.
"It is difficult to comment on such a distorted night. However, if you miss six or seven chances in front of the goalkeeper but concede three goals in three counter-attacks it becomes tricky," Napoli coach Walter Mazzarri told Mediaset TV.
"It's clear it is now going to be difficult but we will try anyway to turn the tie around and do something extraordinary."
Europa League holders Atletico, who finished behind Plzen in their group, were also upset at home by Rubin Kazan.
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.
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."
Anzhi Makhachkala beat Hannover 3-1 in Russia in their first leg.
Samuel Eto'o, four-times African player of the year who has won the Champions League three times with Barcelona and Inter Milan, was on target and missed a penalty for big-spending Anzhi after Hannover had taken the lead midway through the first half.
The Germans drew first blood when Hungarian Szabolcs Huszti scored only for Eto'o to level after 34 minutes and Odil Akhmedov to put Anzhi in front three minutes after the restart.
Eto'o missed a penalty just short of the hour mark but Mbark Boussoufa gave the Russians a sizeable 3-1 lead after 64 minutes.
"We played a good match considering we're only in the third week of preparation (for the re-start of the Russian league season) while our opponents have their season in full swing," Anzhi coach Guus Hiddink told Russian television NTV Plus.
Three Premier League sides were in action: , and Tottenham beat Lyon 2-1 at home.
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.
Borussia Moenchengladbach and Lazio drew 3-3 in the game of the night, the Germans coming from 2-1 down to lead only for the Italians to level in the dying seconds.
There were impressive wins for Spanish club Levante, who beat runaway Greek league leaders Olympiacos 3-0 at home and Ajax, 2-0 victors against former European champions Steaua Bucharest in the Netherlands.
Champions League dropouts Benfica won 1-0 at German club Bayer Leverkusen, Oscar Cardozo on target for the Portuguese just after the hour while Dynamo Kiev and Bordeaux shared the honours in a 1-1 draw in Ukraine.
Belarusians BATE Borisov drew 0-0 at home with Fenerbahce, who were reduced to 10 men after four minutes when Portuguese midfielder Raul Meireles was sent off.
Meireles had an 11-match ban for spitting at a referee in the Turkish league in December reduced to four games on appeal.
In the later matches there was a 2-0 win for Basel over Dnipro Dnipropetrovsk while Stuttgart drew against Racing Genk.