Diniyar Bilyaletdinov headed the rebound to force goalkeeper Andreas Isaksson into a diving save.
Yakubu latched on to a Diniyar Bilyaletdinov pass and curled in a shot to put Everton in front.
Cahill found space in the six-yard box to nod in Leighton Baines' cross after Diniyar Bilyaletdinov had gone close.
The Toffees, without their top scorer Tim Cahill, relied on Saha, Rodwell, Marouane Fellaini and Diniyar Bilyaletdinov to provide the bullets.
Walker was caught napping near the half-way line and dispossessed by Diniyar Bilyaletdinov, who played the ball into the path of Osman.
Yet the Mersysiders held out once more and soon grew in confidence, substitute Diniyar Bilyaletdinov crossing from Coleman to power a header at Cech.
With two minutes left, Russia almost got a consolation goal but Casillas made a stunning save to deny Diniyar Bilyaletdinov's header from Andrei Arshavin's cross.
The Russians had threatened to dominate possession early in the second half and had a couple of chances on goal through substitute Vladimir Bystrov and Diniyar Bilyaletdinov.
Everton manager David Moyes was forced to make a change on the hour when he introduced Diniyar Bilyaletdinov after Steven Pienaar was carried off on a stretcher.
Cech was the first stopper called into action after the restart, tipping over a miscued cross from the recalled Diniyar Bilyaletdinov that almost crept under his crossbar.
Biimingham's five-game winning run was ended in a 1-1 draw at Everton as Diniyar Bilyaletdinov fired Everton ahead in the fifth minute but Sebastian Larsson equalized in the 22nd.
The Bees slowly settled and MacDonald headed over before the home side had shouts for a penalty waved away after Diniyar Bilyaletdinov ran into the back of Myles Weston.
But when Yakubu hit a square ball to Diniyar Bilyaletdinov, the Russian's left-footed volley from distance was hit with tremendous timing, and only just disappeared over the top of Cesar's crossbar.
Everton boss David Moyes, who fielded new signings Distin and Russia winger Diniyar Bilyaletdinov, later revealed the club have agreed a fee with Spanish side Atletico Madrid for defender Johnny Heitinga.
Everton denied Wolverhampton Wanderers a second away victory since being promoted as Russian winger Diniyar Bilyaletdinov scored his first goal for the club in the 88th minute to cancel out Kevin Doyle's 75th-minute strike.
The Toffees' injury problems are mounting ahead of Sunday's Premier League match against Bolton, with Leighton Baines suffering a calf problem before the Benfica tie and winger Diniyar Bilyaletdinov finishing the game with a strapping on his thigh.
Neill, who also held talks with Atletico Madrid of Spain and was linked with a move to Turkey's Galatasaray, is the fourth permanent addition to boss David Moyes' squad, following Sylvain Distin, Diniyar Bilyaletdinov and John Heitinga to Goodison Park.
Diniyar Bilyaletdinov's thunderous strike pulled Everton level within three minutes of Berbatov's goal and both Louis Saha and the excellent Landon Donovan wasted opportunities to put them ahead but they were not to be denied as they more than matched United after the break.
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