Abou Diaby put Arsenal into an early lead but Sami Hyypia lost Phillipe Senderos to head an equaliser.
Striker Emile Heskey scored a brace for the Reds as Bruno Cheyrou, Sami Hyypia and Salif Diao also scored.
Tony Kroos' free-kick found Sami Hyypia, who headed into the path of Kiessling and he volleyed home from close range.
But with Sami Hyypia and Alvaro Arbeloa having left Liverpool this summer, injury problems may force Benitez to increase his bid.
Former Liverpool defender Sami Hyypia made it 3-0 after 39 minutes, with Felix Bastians pulling a goal back midway through the second half.
Chelsea boss Avram Grant surprisingly gave Florent Malouda the nod on the left flank, while Liverpool dropped Sami Hyypia and drafted in Alvaro Arbeloa.
Diouf latched on to Sami Hyypia's weak back header early on, but Jamie Carragher managed to avert the danger just in the nick of time.
But Liverpool captain Sami Hyypia was his usual model of unruffled calm as Liverpool showed why their defence has conceded the fewest goals in the Premiership.
Birmingham created two chances in a minute, first when Christophe Dugarry was clear after a Sami Hyypia mistake and then when Lazaridis got in a flicked header.
The only previous winner in the shortlist is Newcastle captain Alan Shearer, with Liverpool defender Sami Hyypia and Manchester United striker Andy Cole also in the hunt.
Liverpool duo Sami Hyypia and Jari Litmanen will both start for them, the latter desperately trying to impress Anfield boss Gerard Houllier enough to give him a game.
In the summer of 1999, Houllier bought six players, including defenders Sami Hyypia and Stephane Henchoz, who have become one of the best central defensive partnerships in Europe.
There could have been late drama when Sami Hyypia's mistake gifted the ball to Dave Edwards in the Finland box but Bolton keeper Jaaskelainen reacted quickly to deny him and Wales who will finish fourth in the group.
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