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.
Photos: Salman Khan returns from Jodhpur to Mumbai
Pics: Sidharth Shukla-Rashami Desai's sizzling chemistry at TV show launch
Ooh La Lana! WWE Diva flaunts sexy curves in these 30 pictures
15 'peach' perfect photos of Priyanka Chopra at People's Choice Awards 2017
62 going on 16: These photos of Rekha prove she is 'forever young'