The five-times champion smashed 15 aces and 44 winners in all as he followed up his confident first-round win with another immaculate display, wrapping up victory in just 90 minutes.
"I enjoyed it a lot, it was a great match for me," Federer told the packed crowd inside the cavernous Arthur Ashe Stadium.
"I always enjoy it when I have the chance to come out here at night and make it a match for you guys."
In the last game of the match, Phau had the temerity to hit one reflex backhand pass off a Federer smash that the Swiss agreed had been the shot of the match.
"Bjorn had some incredible shot-making," Federer said. "That backhand was ridiculous really.
"When it's against you, you don't really enjoy it but I was leading so it was OK. It was a lot of fun."
World number 83 Phau was once renowned as the fastest player on the Tour but, at 32, his speed is on the wane and Federer had him on the stretch from the start.
The Swiss broke in the fourth game to establish control and never loosened his grip on the match as he cruised through to a clash with Fernando Verdasco, who beat fellow Spaniard Albert Ramos 7-6(4) 5-7 7-6(5) 6-4.
Federer has won all four of his meetings with Verdasco but knows better than to underestimate him when they play on Saturday.
"He's a great player," he said. "He's been around a long time and had his share of big wins so I am not going to look any further than him."
Frenchman Jo-Wilfried Tsonga became the first high-profile casualty in the men's event at when he was upended 6-4 1-6 6-1 6-3 by Slovakian Martin Klizan in the second round.
The fifth seed produced a strangely lacklustre display as he was outplayed by the world number 52 and suffered his earliest-ever US Open exit.
The left-handed Klizan had never been beyond the second round at a grand slam event before but he surprised Tsonga with some inspired tennis.
Tsonga rallied from 4-1 down in the fourth set to 4-3 but the 23-year-old Klizan held his nerve to seal the biggest victory of his career.
Tsonga said he was fully fit and healthy but that for some unknown reason he could not find his best form when he needed it.
"I'm not very satisfied," Tsonga said. "I lost second round. I'm used to playing the round of 16 or quarter-finals, sometimes semis.
"(But) it's tennis. Today I didn't play my best tennis and my opponent was better than me the whole match I think, and that's it."
"Today I was not in a good shape and I didn't play good tennis," he added. "It seemed like I couldn't hit the ball hard enough to put my opponent out of position.
"I don't really know why it was like this today but sometimes it happens with me."
Klizan now meets Jeremy Chardy after the 32nd seed Frenchman beat Matthew Ebden of Australia 6-4 6-2 6-2.
American Mardy Fish risked following Tsonga out, but survived a huge scare as he recovered from two sets down to beat Russia's Nikolay Davydenko and reach the third round.
The 23rd seed began slowly but found his form just in time to clinch a 4-6 6-7 6-2 6-1 6-2 victory and become the 10th man in the tournament to win from two sets down.
At 31, former world number three Davydenko has slipped to 47th in the rankings but a shock looked possible when he won the second-set tiebreak.
But Fish found his form just in time and punched the air when a Davydenko forehand landed wide to set up a clash with number eight seed Gilles Simon of France, who beat Taiwan's Jimmy Wang 6-4 4-6 6-4 6-4.
Andy Murray's next opponent will be Feliciano Lopez, the Spaniard securing his place in the third round with a 6-4 6-1 6-7(5) 3-6 7-5 win over compatriot Pablo Andujar.
Sixth seed Tomas Berdych wasted no time in booking his place in the third round with a 6-1 6-4 6-2 win over Estonia's Juergen Zopp, while number 11 seed Nicolas Almagro saw off Philipp Petzschner 6-3 5-7 5-7 6-4 6-4.
Berdych now plays Sam Querrey, who downed Spain's Ruben Ramirez Hidalgo 6-3 6-4 6-3, while Almagro meets Jack Sock of the US after his 6-2 6-2 6-4 win over Flavio Cipolla of Italy.
Another American, James Blake, turned back the clock to cruise past 24th seed Marcel Granollers 6-1 6-4 6-2 and book a date with 15th seeded Canadian Milos Raonic, who saw off Paul-Henri Mathieu of France 7-5 6-4 7-6(4).
And 12th seed Marin Cilic saw off Daniel Brands of Germany 6-3 6-2 5-7 4-6 7-5 to set up a clash with Kei Nishikori, the 17th seed, who beat American Tim Smyczek 6-2 6-2 6-4.