Emile Heskey headed on a long punt by Friedel, latched on to the return pass from from Gabriel Agbonlahor and volleyed into the net from 15 yards for the game's lone goal.
Aston Villa is two points ahead of fourth-place Cheslea, which can move back ahead of Villa if it beats Middlesbrough tomorrow.
Clint Dempsey played the full 90 for Fulham, which fell, 1-0, at Sunderland. Fulham is in 10th place.
In the German Cup, Gregg Berhalter went the distance as second division 1860 Munich was eliminated in the round of 16 with a 3-1 loss to top tier Hamburg SV.