Russian side beat Premier League visitors by one goal to nil with a goal from Lacina Traore.
Anzhi defeat Liverpool to take top spot in Europa League group
Liverpool conceded top spot in Group A to Europa League opponents Anzhi Makhachkala after defeat in Moscow.
Giant striker Lacina Traore scored a brilliant individual goal as the visitors switched off seconds before half-time.
The result, the Reds' first-ever away defeat in the group stage and only their third loss in 22 European matches, allowed the Russian club to assume pole position.
Anzhi may play 1,600 kilometres away from their home in Dagestan because of security issues but they remain strong on Russian turf and made it five successive European home wins.
It was always going to be a tough assignment for Liverpool as manager Brendan Rodgers, with Sunday's trip to Chelsea in mind and unperturbed by a weakened team's Capital One Cup exit against Swansea last week, opted to leave his big-name stars at home.
As a result he selected nine Englishmen, in a starting XI with an average age of just under 24, in a 3-5-2 formation.
It meant Conor Coady, who captained England Under-17s to their first European Championships title in 2010, made his debut in an icy-cold Lokomotiv Stadium.
The Liverpool-born 19-year-old has progressed through the club's academy and was given his chance having been an unused first-team substitute three times.
Striker Adam Morgan, 18, was making only his second start but, having been prolific throughout youth level Rodgers remains hopeful he will eventually make the step up and he was given the difficult job of leading the line.
At the other end of the scale Joe Cole, on his 31st birthday, struggled to make an impact again after a woeful 45 minutes against the Swans.
The first half was a typically cagey European affair with chances at a premium.
All of which made it all the more remarkable that when presented with a shooting opportunity Jordan Henderson declined in the 23rd minute.
The 22 year old spoke before the match about wanting to prove he has a future at Anfield but he will need to improve his decision making if that is to be the case.
Morgan showed good strength to hold off Odil Ahmedov and thread a pass through but from a 45-degree angle he opted to cut the ball back to the striker.
It probably showed a lack of confidence but chances in Europe do not come around that frequently and it was a waste.
Contrast that with former Barcelona forward Samuel Eto'o, Anzhi's £330,000-a-week (Dh1.9 million) marquee signing, who forced Brad Jones into a good save from Yuri Zhirkov's cross after the ex-Chelsea player had robbed Andre Wisdom near Liverpool's right touchline.
Henderson flicked on a tame near-post header from Downing's cross and Cole nodded Downing's inswinging free-kick wide before, in added time, Liverpool lapsed.
Traore brilliant spun Sebastian Coates with a left-footed touch and then lobbed Jones with his right for his fourth goal in six matches.
Cole at least made it out for the second half, which was more than he did last week, and set up Morgan to fire into the side-netting soon after the restart.
Eto'o replied with a curling shot which Jones claimed comfortably diving to his left while Traore and Rasim Tagirbekov flashed shots just past the post as the game began to open up.
Substitutes Suso and Dani Pacheco, on for Morgan and Coady, gave the forward line some more youthful impetus but it was the hosts who remained the more threatening with Jones making another good save from Traore's powerful header.
Cole's last contribution before being replaced by Oussama Assaidi was to force a close-range save from Vladimir Gabulov after he had fumbled Suso's shot.
But Traore should have finished off Liverpool when put clean through by Eto'o but he rolled his effort wide of the upright.
Henderson had a late chance to equalise but ballooned his shot well over.
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