Federer had only once failed to reach the Last Four in 11 previous appearances at the season-ending event and he recovered from a set and a break down, and then 3-0 down in the final set, to subdue the Argentine fourth seed and maintain his impressive record.
The six-time Tour Finals champion qualified in second place in Group B behind defending champion Novak Djokovic and will face World No 1 Rafael Nadal in today’s semi-finals at London’s O2 Arena.
“A lot of coming from behind, trying to get back into the match, and it was amazing that I was able to pull it off,” Federer said. “I could never play free flowing tennis. I fought hard, maybe got a bit lucky at times.”
Nadal tops Group A
Earlier, Rafael Nadal secured top spot in Group A with a victory over Tomas Berdych that also sent Stanislas Wawrinka into the semi-finals.
Nadal had already qualified for the last four of the season-ending event and his 6-4, 1-6, 6-3 win against Berdych ensured a first place finish with a 100 percent record from his three group matches.
Czech fifth seed Berdych could have gone through with a win, but instead he was eliminated and Swiss seventh seed Wawrinka progressed to the Last Four following his 6-7 (3/7), 6-4, 6-1 victory over Spanish third seed David Ferrer earlier on Friday.