The 17,500-capacity crowd crammed into the O2 would have been expecting something longer from the eagerly anticipated 26th clash of the great rivals but the 60 minutes of magic Federer served up will live long in their memories.
Blazing winners to all corners of the court, the Swiss 16-times grand slam champion was simply unstoppable as he recorded his most emphatic victory against the man who had beaten him in 17 of their previous encounters.
"This win ranks high because it's against my biggest rival, probably," Federer, whose game looked sharper than ever despite him turning 30, told reporters.
"It was a great match for me from start to finish. I've felt the power of Rafa in the past, so this is a great match for me, a nice win."
World number two Nadal now faces a win or bust clash with Jo-Wilfried Tsonga on Thursday in his final Group B match after the dangerous Frenchman produced fireworks of his own to beat American Mardy Fish 7-6 6-1 and stay in contention.
"It's not the moment to say goodbye. If I win my next match I will be in the semi-finals," Nadal said. "I just have to accept today he played too good for me."
Federer's dazzling display softened the blow for the home crowd and organisers after local favourite Andy Murray withdrew when his superb season was cut short by a groin injury.
Murray, the world number three, announced he was pulling out after aggravating the injury during his opening Group A defeat by Spain's David Ferrer on Monday.
Serbia's world number nine Janko Tipsarevic, the on-site alternate, will take the Briton's place for the remaining matches.
There was something of a novelty value about the evening match as it was the first time the two dominant players of the last decade had clashed with neither at number one in the ATP rankings and the first time they had met in round-robin play.
Federer trailed 17-8 in their head-to-head record but had won all three previous meetings indoors, including last year's final at the O2, and once again the court proved perfect for his game as winners flowed from his strings like liquid gold.
There was no real hint of what was to come as the first five games went with serve.
Federer, bidding for a record sixth title at the tournament in three different cities, took charge in the sixth game when he prevailed in a 33-shot exchange on break point to lead 4-2 and from that moment never looked back.
He needed just 32 minutes to seal the first set and, try as he might, Nadal was powerless in the face of the onslaught as Federer swept to a victory every bit as ruthless as Nadal's thrashing of the Swiss in the 2008 Roland Garros final when he offered up just four games in three sets.
"We've played so many times, sometimes it just derails for you, like it derailed for Rafa today and it did for me at the French Open," Federer said.
"You know what good front-runners the top guys are. Once you start rolling, it's hard to stop the player. Next thing you know, you're facing a debacle."
Nadal, winner of 10 majors but never the season-ending title, can still redeem himself although Tsonga will fancy his chances after a convincing display against weary debutant Fish who can no longer reach the semis.
Tsonga, sporting a pair of bright red tennis shoes, stormed through the last six games in swashbuckling fashion although Federer still tips Nadal to progress.
"You can never count out Rafa," he said of the match which has now become a traditional knockout. "It's an open match to a degree but I still favour Rafa because of who he is."
Murray can only rest and start preparing for next season after a long campaign, in which he reached the semi-finals of all four grand slams and won five titles, caught up with him.
"It was one of those things where you kind of hope that things are going to get better, but the reality was that wasn't ever going to happen," a glum-looking Murray told reporters.
"Yesterday I was really unhappy on the court. I wasn't enjoying it at all. I couldn't give anywhere near my best."
World number one Novak Djokovic seeks his second Group A victory on Wednesday against Ferrer, while Tomas Berdych, who lost a tight three-setter to Djokovic on Monday, faces Tipsarevic who will be making his debut in the elite event.