The 20-time Grand Slam victor and reigning champion Federer plays 13th seed Borna Coric of Croatia in Saturday's other semi-final.
Novak Djokovic's return to the summit of world tennis appears nearly inevitable after he booked his place in the final of the Shanghai Masters following a straight sets victory over Alexander Zverev.
Having needed three sets to get beyond Daniil Medvedev and Roberto Bautista Agut in his last two outings, Federer appeared in danger of needing a decider again when he trailed 4-1 in the second-set tie-break.
For this first match, Djokovic is a solid [1.37] favourite to make the final, and rather surprisingly for two top-five players, they've only had one previous meeting, which Zverev took on the clay in Rome past year without facing a single break point.
It was a good show of sportsmanship by both players
'That's the best match I've seen him play [since his comeback],' he said. "It's going to be definitely a close match".
As the Shanghai Masters continues, Saturday morning sees the semi-finals take place and back with his thoughts on the action is Dan Weston.
The top seed turned on the style in Friday's last match on court, recording a 6-4 7-6 (7-4) victory after one hour and 51 minutes. Zverev is the fifth player to qualify for the season-ending tournament in London, joining Rafael Nadal, Roger Federer, Novak Djokovic and Juan Martin del Potro in the eight-player field. Zverev couldn't get through the defence of Djokovic whatsoever today.
About his co-operation with Ivan Lendl, Zverev added: 'We are still working together.
"Last year was the first time I kind of broke through to the top 10 and was a top-five player".
'You are always trying to stay centered and balanced. There is still a lot more tennis going on till the end of the year.
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