The Premier League giants were outplayed by the League One leaders for much of the third-round tie but Ngog netted against the run of play after 65 minutes.
Leeds spurned a number of chances as Elland Road enjoyed a big-game atmosphere once again, but a lack of composure in front of goal cost them.
Leeds striker Jermaine Beckford endured a particularly frustrating night as he missed several good chances and had a goal in the first half disallowed.
It was Liverpool's first visit to Leeds since their hosts were relegated from the top flight in 2004 but the atmosphere generated by the 38,168 crowd rekindled memories of a once intense rivalry.
But Liverpool won it when Javier Mascherano mis-hit a shot from the edge of the area but Ngog reacted quickly and seized on the ball to tuck past Shane Higgs.