Murray had beaten Robin Soderling 6-2 6-4 yesterday afternoon and his Group B rival was just as emphatic, dispatching the seventh seed 6-1 6-4 at the O2 Arena, although not without a scrap in the second set.
Federer, who will play Murray tomorrow, said: "It was a really tough match for the scoreline. He's a great player so I was really happy I was able to come through."
Federer has been in good form lately and he certainly looked like a man in a hurry as he raced through the opening four games, dominating both from the back of the court and on the occasions he chose to come to the net.
It seemed very ominous for Ferrer when the world No 2 moved 40-0 ahead in the fifth game but the Spaniard is a renowned fighter and he won five points in a row to retrieve one of the breaks.
Ferrer, playing his first World Tour Finals match since losing to Federer in the 2007 final, battled hard in an attempt to hold serve for the first time in a lengthy sixth game but three double faults ultimately proved his undoing as the four-time champion moved 5-1 in front.
And serving out the set was no problem for Federer, who hardly needed the good fortune of a net cord on the decisive point.
Ferrer at last found some winners to save yet more break points in the third game of the second set but he was under pressure every time he stepped out to serve and at 2-2 he crumbled.
Federer was forced to save two break points in the following game, before serving out the match.