The Reds went into the game in Romania holding a narrow one-goal advantage thanks to a David N'Gog strike last week and the Frenchman led the Reds' frontline again.
The early minutes saw few clear openings at either end, although the home side seemed more positive in their approach.
Sorin Frunza's shot curled just wide of target, before home keeper Giedrius Arlauskis was forced to push away a Steven Gerrard effort.
Nineteen minutes in the tie was all-square as Razvan Paduretu swung in a right-foot corner from the left and Bruno Fernandes rose unmarked to head home from six yards out.
However, Liverpool hit back to equalise on the night when Ryan Babel miskicked when well placed and the ball was cleared to 25 yards out, from where Javier Mascherano arrowed a superb right-foot shot into the back of the net.
The Reds then took a 2-1 lead on the night and a two-goal aggregate advantage when Babel took down a Gerrard free-kick and in one quick motion prodded home a right-foot shot from six yards out at the far post.
The second half began with the visitors on top and 12 minutes after the restart Liverpool made sure of a place in the last 16 with a third goal of the evening.
Yossi Benayoun's driving run into the area ended with the ball falling at the feet of Gerrard and his low drive sneaked into the net through the legs of home keeper Arlauskis.
Unirea kept plugging away as the Bucharest pitch began to cut up badly, but the tie had long since been decided in Liverpool's favour.