The world number one - bidding for a fourth successive Swiss Indoors title - shook off the rust from a six-week break to roar through and a date with Italian Andreas Seppi in just 66 minutes.
Federer's march to victory was preceded by an operatic performance with massed choir and selections from Aida as his hometown honoured three straight titles at the St Jakobshalle by the world-famed native son.
"I felt so good out there," said the winner, who needed three match points to go through after earning the first two winning chances with his 11th and 12th aces of a quick evening.
"This was my longest pause, even longer than in the close season. But I really needed it and it was worth it," said the winner of a first French Open title and sixth Wimbledon title this season.
"It's so great to be playing in Switzerland. I haven't done it for a year and I really missed it.
"I felt I played a good match and just want to carry on like this."
Federer improved to an overwhelming 6-0 over Rochus, who lost to Marcos Baghdatis in the Stockholm final just over a week ago.
The Swiss top seed broke in the sixth game of the 29-minute first set, then fired his fifth ace for a 5-2 lead before securing the opening lead.
In the second, Federer went ahead 3-2 and was untroubled save his minor niggles in closing out the straightforward victory.
Federer admits that Basel is the event closest to his heart after getting his start here as a ballboy a decade and a half ago.
The top seed has not played since helping his nation retain their place in the Davis Cup World Group with a win over Italy in September -Federer chose to rest rather than play the autumn tournaments in Asia.
The 15-time grand slam champion has laid low and got to know his three-month old twin girls as he assumed his additional new role as a father. He was unable to help himself as he bragged about his daft hand with a dirty nappy.
"I have an unbelievable technique," he said to laughter - mainly from his wife sitting in the stands.
Federer has not lost in Basel since the second round in 2003 when he was beaten by Croatian Ivan Ljubicic.
The Swiss who plans to go flat-out through this week, the Paris Masters starting next Monday and the year-end eight-man World Tour Finals in London, brings a 55-8 record this season to the court, with titles in Paris and Wimbledon as well as the Madrid and Cincinnati Masters events.
Fellow Swiss Stephane Bohli failed to give the home crowd a winning start on the day, with the number 148 journeyman losing 4-6, 6-1, 7-5 in the first-round to Italy's Seppi.
Bohli, now 0-4 at the ATP level this season, sprang a surprise on Seppi by winning the first set before the 51st-ranked Italian pulled his game together.
In the day's opening contest, Frenchman Florent Serra survived 28 aces off the racket of serve machine Ivo Karlovic but still subdued the Croatian 7-6 (7/5), 6-4.