UEFA Cup holders CSKA Moscow needed two late goals from Brazilian playmaker Daniel Carvalho to make a winning start to their defence on Thursday.
Carvalho scored twice in three minutes as CSKA defeated Denmark's FC Midtjylland 3-1 in their first round, first leg clash in front of a handful of fans.
Forced to play behind closed doors as punishment for their fans' behaviour in the home leg of the semi-final against Parma last season, Russia midfielder Rolan Gusev gave CSKA a 21st-minute lead but it was quickly cancelled out with a deflected goal by Ghanaian Razak Pimpong.
Carvalho, whose virtuoso performance inspired CSKA to become the first club representing Russia to win a European club final when they defeated Portugal's Sporting in May, struck in quick succession on 76 and 79 minutes.
Dinamo Bucharest inflicted a crushing defeat on hapless Everton as the Premier League side, denied a Champions League place by Villarreal, capitulated in the Romanian capital to suffer their heaviest European defeat.
Level 1-1 at the break after Joseph Yobo had cancelled out Claudiu Niculescu's opener, Dinamo led again through Ianis Zicu and then rammed home their advantage through Florentin Petre and two from substitute Florin Bratu.
Dutch league leaders and last season's UEFA Cup semi-finalists AZ Alkmaar also shipped five goals in a shock 5-3 reverse at Krylya Sovietov Samara, who languish in 13th place in the 16-team Russian premier league.
Samara, who have lost a host of key players during the season because of financial difficulties, had been pegged back to 4-3 by Barry van Galen's goal five minutes from time but Anton Bober restored the two-goal cushion in stoppage time.
On a good night for Russian sides, league leaders Lokomotiv Moscow came from behind to earn a 2-1 win away at Brann Bergen.
Feyenoord, who like AZ have won their opening four games in the Dutch championship, were left with work to do in Romania in the second leg after Rapid Bucharest battled to a 1-1 draw.
In another game to be played behind closed doors owing to a UEFA punishment, the 2002 UEFA winners led through Dirk Kuijt's fine lob just before halftime but substitute Ciprian Vasilache earned Rapid a draw from the penalty spot 15 minutes from time.
Sporting began their UEFA campaign with a 2-1 win in Sweden over Halmstad, goals from Brazilians Wender and Deivid handing the Lisbon side victory after they had fallen behind.
FC Copenhagen held former European Cup winners Hamburg SV to a 1-1 draw in Germany.
Rafael van der Vaart, Hamburg's 5.5 million euro signing for the new season, flicked in from Thimothee Atouba's low cross eight minutes before halftime but Copenhagen equalised quickly, with South African international Elrio van Heerden sweeping in from the edge of the box in the 40th minute.
AS Roma defender Christian Panucci scored twice in a 5-1 demolition of Greek side Aris Salonika while goals from midfielder Olivier Kapo, on loan from Juventus, and Emmanuel Adebayor handed Monaco a 2-0 home win against Willem II.