Fabio Quagliarella put Udinese, currently in second place in Italy's Serie A, in front in the 12th minute before Spartak's Argentinean defender Clemente Rodriguez leveled with a well-taken shot. However, Rodriquez fouled Simone Pepe in the 25th minute in the penalty area, and it was Quagliarella who stepped up to put the Italians back in the lead.
Spartak, playing their first Group D game, went close on a number of occasions in the second-half, with Vladimir Bystrov looking dangerous, but Udinese came away with three points to add to the three they earned from their 2-0 win over England's Tottenham Hotspur on October 23.
"We played a good game, if you don't take the result into account of course," said Spartak coach Michael Laudrup.
In the group's other game, Tottenham Hotspur beat Dynamo Zagreb 4-0 at home. Former Spartak striker Roman Pavlyuchenko, who signed for the Londoners in the summer, did not play as he is cup-tied after turning out for Spartak in an earlier Champions League qualifier.
In the Netherlands, two goals from CSKA's Brazilian striker Vagner Love helped the 2005 UEFA Cup champions to a 3-1 win over Feyenoord.
An own goal by Giovanni van Bronckhorst gave CSKA the lead in the 14th minute. However, he made up for his mistake a quarter of an hour later with a calmly-placed shot after the CSKA defense had done a disappearing act.
Van Bronckhorst turned villain again in the 40th minute, a weak header sending Vagner Love through to slot home CSKA's second, and it was Love who sealed the win for the Moscow club with a fine individual goal with nine minutes on the clock.
A late red card for CSKA midfielder Yevgeny Aldonin slightly marred the win, but the Russian club will be pleased with a professional and confident performance that confirmed them one of the favorites to lift the tournament.
"It was a tough match, and Feyenoord used everything possible to try and get the result," said CSKA trainer Valery Gazzayev.
CSKA, who beat Spanish side Deportivo 3-0 in Moscow in their opening match, now top group H with six points. As the first three teams in the group go through to the play-off stages, the Russian club could probably even afford to lose their last two matches and still make progress.
