Ouedec struck in the 63rd and 85th minutes to wipe out two outstanding first-half goals by the Spartak captain, Yuri Nikiforov, which had brought the Russians firmly back into contention after they they lost the first leg 2-0 in France two weeks ago.
The French international striker, wearing gloves because of the cold, scored his first goal by running on to a long pass which evaded two Spartak defenders and slipping the ball calmly past the Spartak goalkeeper, Ruslan Nigmatullin.
Although Spartak dominated possession, even after conceding a goal, Ouedec had the last word with a left-footed drive from close range which gave Nigmatullin no chance.
The defeat marks the end of the road for a fine Spartak side, who have already surrendered their Russian League title to Spartak Vladikavkaz. After qualifying for the quarter-finals several top players left the club, including Sergei Yuran and Vassili Kulkov, who are both now at Millwall.