Derby 1 Liverpool 2: Steven Gerrard's unrelenting determination earned Liverpool all three points against a Derby side with every right to feel hard done by at Pride Park.
Liverpool had been comfortably the better side in the first half and Fernando Torres scored his 15th goal in 18 games.
But following on from their outstanding efforts to force a draw at Newcastle at the weekend, injury-ravaged Derby showed magnificent spirit to force their way back into the game with a second-half equaliser from Jay McEveley.
They battered away at Liverpool for much of the second period, with rookie goalkeeper Lewis Price outstanding even if his side finished with 10 fit men — Robert Earnshaw was by then a limping passenger.
Liverpool at times were dreadful, but captain Gerrard showed how to fight by instigating an 80-yard move, finishing it off by bundling the ball past Price in the dying minutes.
Derby believed they had good shouts for two late penalties, but they ended with nothing.
A flash of genius after 12 minutes saw Liverpool go ahead. Torres took a pass from Babel, pushed the ball through Darren Moore's legs before side-stepping Dean Leacock and blasting a 15-yard strike past the helpless Price.
Two home players collided on 24 minutes, leaving Stephen Pearson hurt. Liverpool stormed away and Babel should have scored when John Arne Riise's cross reached him at the far post. But the effort finished in the crowd.
Derby dominated the opening exchanges of the second half with Giles Barnes coming into the game. Price saved well to his left from an Alonso effort, but Derby still came forward with belief and a ferocity in the challenge that forced Liverpool back.
And from a 67th-minute free-kick, Derby were level to send Pride Park wild. Eddie Lewis lifted a free-kick into the box from the right and it was allowed to bounce around before McEveley fired past Jose Reina.
McEveley was then booked for a foul on Voronin before Liverpool sent on Dirk Kuyt for Babel. Gerrard fired wide from the edge of the box, before more injury problems hit Derby with Earnshaw's injury.
Price made a stunning save to turn away an Alonso 30-yard strike after 82 minutes, and then Torres fired high over as Liverpool continued to come forward.
Barnes missed with a close-range diving header, the game now on a knife-edge as Liverpool came forward in desperation.
Gerrard hit the bar from 20 yards before he put Liverpool ahead in the 89th minute. Price made another fine save from Torres, but the ball bounced out for the Liverpool skipper to force home, having started the move 80 yards away in his own half.
