Serbo-Montenegrin striker Mihajlo Pjanovic scored a brace for the Russian hosts, with Ukrainian Maxim Kalinichenko and Alexander Pavlenko scoring in the Lokomotiv Stadium.
Dinamo Bucharest's night was made worse with a minute remaining as Ionut Badea was sent off for a second bookable offence.
Czech side Teplice scored an excellent 2-0 away over Dutch giants Feyenoord at De Kuip.
Things went wrong for the Rotterdam side when Gill Swerts was sent off for a professional foul inside the first two minutes of the match.
A minute later, Michal Dolezal put the visitors in front before Jan Rezek made it two after the break, as Teplice will have the upper hand for the second leg in Czech Republic in three weeks' time.
Ukrainian side Dnipro Dnipropetrovsk earned an excellent 2-0 away win at Croatian giants Dinamo Zagreb in their first leg tie.
Oleg Venhlinsky put the visitors ahead after eight minutes and Roman Maksymiuk sealed victory with a second five minutes from time in the Maksimir Stadium.
Bulgarian side Levski Sofia took the upper hand in their tie with a 2-2 away draw in the first leg at Czech club Slavia Prague (pictured).
Pavel Kuka gave Slavia a 1-0 half time lead but Levski equalised through Georgi Ivanov in the second half.
The home side were reduced to ten men with five minutes remaining after Karel Pitak was sent off for a second bookable offence.
Both sides then scored again in injury time, with Levski briefly going into the lead through a Martin Muller own goal before Pavel Fort equalised to spare Slavia's blushes on the night.
Norwegian side Valerenga were held to a 0-0 draw in Oslo by Polish club Wisla Krakow, who played the last seven minutes of the match with ten men after Damian Gorawski was sent off for a second bookable offence.
Turkish club Genclerbirligi, who advnaced from the first round by knocking off Blackburn Rovers, were held to a 1-1 home draw in the first leg by Portuguese giants Sporting Lisbon.
The visitors took the lead five minutes after the break through Da Silva Liedson but Veysel Cihan was able to equalise for the Ankara-based outfit six minutes later.
Greek club PAOK Salonika were held to a 1-1 home draw by Hungarian outfit Debrecen.
Loukas Karadimos gave PAOK the lead after 11 minutes but Debrecen soon equalised when Peter Bajzat scored a quarter of an hour later, as both sides stayed deadlocked in Thessalonika.
Finally, Portuguese giants Benfica ran out comfortable 3-1 winners over Norwegian side Molde at the Estadio da Luz.
A brace from Nuno Gomes and a third goal from Brazilian Geovanni was enough to give the Lisbon club a solid lead for the second leg in Norway, though Molde did score an away goal late on through Daniel Berg Hestad.
Click below for match summaries:
Uefa Cup
Benfica 3-1 Molde
Dinamo Zagreb 0-2 Dnipropetrovsk
Feyenoord 0-2 FK Teplice
Genclerbirligi 1-1 Sporting Lisbon
PAOK Salonika 1-1 Debrecen
Slavia Prague 2-2 Levski Sofia
Spartak Moscow 4-0 Dinamo Bucharest
Valerenga 0-0 Wisla Krakow
