Arsenal continued where they left off after the break and Kolo Toure scored ten minutes into the second half to put the Gunners 2-0 up.
With ten minutes remaining, and the game all but beyond Liverpool's reach, William Gallas headed in the third.
The result leaves Liverpool languishing in 9th place in the Premiership, 14 points behind Man Utd, and still looking for their first away goal in open play.