Federer came out victor in the 'winner takes all' Group B clash and progresses into semi-finals where he will face Group A winner Rafael Nadal.
The six-time champion came from behind to triumph 4-6 7-6 (7-2) 7-5 at London's O2 Arena and Boris Becker told Sky Sports that this win means Federer shows he can play with the best a bit longer.
Becker said: "Well the legend lives for another day.
"After 25 minutes I thought it was going to be a white-wash for Del Potro - he'd managed to win the first set 6-4, he was up a break in the second set, he was up a break in third set and somehow Federer found the energy when he needed it most.
"It wasn't pretty at all times but it was successful."
Fellow Sky Sports tennis expert Annabel Croft agreed with Becker's sentiments and admits she feared for the outcome of the result in the first set.
"At the start when he was down 5-1 it was actually quite painful viewing and you thought my goodness he's going to get absolutely crunched off the court here," added Croft.
"But you have to admire such strength of character from the man because each set he found a way to get himself back involved and it took 2 hours and 27 minutes to finally make the breakthrough and get on top of the match.
"He did it in style, he had the crowd behind him and it was extremely close, but what a match."
This win eases pressure on the 17-time Grand Slam champion, who has had a season of poor results and faced in-form Del Potro, who had beaten the Swiss star at his home tournament in Basel just last month. Greg Rusedski added to the analyses and says he felt Federer's brilliant comeback was down to him relaxing his game.
Rusedski said: "The key was Federer really relaxing and that was when he all of sudden started flowing and got his tennis back, Del Potro had a dip and Federer pounced, he found the big points and that hasn't happened for him this year so he's starting to find his form.
"He deserves to win today and this is a big win in his career, beating back-to-back top ten players, it's starting to flow and do the right things. He's taking the right steps forward and all those Federer fans will be delighted."
Watch every session of the ATP World Tour Finals - which run from November 4-11 - on Sky Sports. Click here for coverage details.
You can catch all the action from the ATP World Tour Finals with a Sky Sports Day Pass. For more information click here