The double strike killed off the match as a competitive spectacle, although JermainePennant flashed in a couple of long-range free-kicks to give Birmingham some hope.
Asamoah Gyan regained the lead for Sunderland after the break, but the visitors sat back and finally buckled under a barrage of long throws and set-pieces, as two JermainePennant free-kicks set up Huth to score twice in the last seven minutes and seal a remarkable recovery.
The Reds are expected to make a bid for Birmingham right-winger JermainePennant, 23, in the near future as they look to add to the new signings of Craig Bellamy, Fabio Aurelio and Mark Gonzalez.
He provided the perfect finish to a delightful Liverpool build-up in the fourth minute, sweeping in at the near post after Jermaine Pennant's neat flick set up Arbeloa for the cross.