The Scot went into the clash with hopes of the straight-sets win that would have booked his spot in the semi-finals but walked off the court 56 minutes later having lost 6-0 6-1.
Murray was two points away from losing 6-0 6-0 for the first time since he was a 16-year-old playing on the lowly Futures circuit. He at least avoided that ignominy but there was no consolation at all to be gained from the single game he managed to win against a player he has so often frustrated in the past.
In a tournament of one-sided matches, Murray now has the unwanted distinction of having suffered the worst defeat since the event moved to London’s O2 Arena in 2009, while it was his heaviest loss for seven -and-a-half years.
Federer tried to conjure up some crumbs of comfort for his vanquished opponent, saying: “Clearly I’m very happy to play a good match today. I knew I was qualified so maybe I went in a bit more relaxed. It’s not the way I thought it was going to go but there’s always next year for Andy and hopefully he can have a good season.”
Kei Nishikori’s 4-6 6-4 6-1 victory over alternate David Ferrer earlier on meant Murray knew he could not lose a set if he wanted to pip the Japanese player to a spot in the last four. Nishikori said he would not be following the match because he wanted a “good dinner”, and he would barely have tucked into his starter when his progress was secured after a first set which lasted just 24 minutes.
Federer knew before the match he was already through but a set would see him top the group and, in all likelihood, avoid Novak Djokovic in the semi-finals.
He could swing freely while Murray knew he had to be aggressive but he could not land a first serve – just seven in the first set – and too often he found the net or the extremities of the court.
Earlier, Ferrer had stepped in after Milos Raonic pulled out with a thigh injury and played his part in the most competitive match yet.