The teams had an equal share of the possession, but Liverpool created far more chances, suggesting that 1-0 many not have been a fair reflection.
Here, Sports Mole dissects the 90 minutes and brings you some in-depth analysis from a match that saw Liverpool shoot to the top of their Europa League group.
On target 8
On target 5
Was the result fair?
Absolutely. Liverpool bombarded the Anzhi goal throughout and the majority of the play took place in the opposition's final third. If anything, Liverpool should have won by more than one, but scoring goals is exactly their problem at the moment.
Brendan Rodgers's side were impressive all round this evening, lacking only that clinical touch up front. Martin Skrtel and Daniel Agger looked watertight at the back, and the Reds created plenty of chances from midfield, with Oussama Assaidi putting in a particularly impressive shift.
Anzhi Makhachkala's performance
Guus Hiddink's team were tidy in possession, but didn't create many clear-cut chances, which is disappointing considering they had a striker of Samuel Eto'o's caliber up front. The Russians were second best all round, and didn't look like a team who have lost just one game domestically all season.
Sports Mole's man of the match
Oussama Assaidi: The Dutch-Moroccan winger looked sharp and dangerous all evening, striking fear into the heart of the opposition's defence whenever he broke forward. He deserved full marks for his work rate and creativity.
That has to be Agger heading the ball out of the hands of Anzhi keeper Vladimir Gabulov and putting it into the net, an illegal move that saw him booked. You can only get away with doing that if you are the late George Best.
Bas Nijhuis got the majority of his calls right, but he should have awarded Liverpool a penalty in the second half when Assaidi was clearly fouled in the area. Luckly the outcome of the game was not affected by this blunder.
Liverpool: Liverpool have the Merseyside derby against bitter rivals Everton to contend with on Sunday. It will be interesting to see whether Rodgers's decision to field key players tonight will impact on that game.
Anzhi Makhachkala: Anzhi will be looking to continue their impressive form domestically and maintain their position at the top of the Russian league.