"It's going to be a good weekend, dear," he told the crowd of thousands gathered for the three-day festival, which erupted in cheers with the first chords of Beatles tunes like "Eleanor Rigby." It was McCartney's first appearance at a U.S. festival as a solo artist.
In the 2 1/2-hour set, including two encores, McCartney dedicated "Long and Winding Road" and "My Love Does It Good" to his late wife Linda, who died in the Arizona desert 11 years earlier to the day.
"It's an emotional day for me. That's good, that's OK," he said, pounding his chest. "Lot of heart, lot of emotion."
Before a moving performance of "Blackbird," he noted that it had been written in response to the 60s civil rights movement. "Now you've got President Obama. Yeah, you know we've come a long way."
Switching from serious to cheerily self-aware, he led call-and-response chants only to wave them off quickly as "messing around," and dismissed signs held by front-row fans
- including one that asked for his guitar pick.
"No! It's mine!" McCartney said. "Anyway, if I make a mistake, I can blame the signs."
There were mistakes. McCartney was proficient but sometimes out-of-sync with the four-man band backing him. But he clearly enjoyed himself, plowing through songs from his "Fireman" album, "Band on the Run" from the Wings, and Fab Four favorites like "Back in the USSR," "Paperback Writer" and, for the finale, "Sgt. Pepper's Lonely Hearts Club Band."
McCartney launched brightly into "Something" with only his voice and a ukulele he said was given to him by George Harrison, before his band mates and the crowd joined in.
The first day of the festival also featured Morrissey, Leonard Cohen, the Hold Steady, Franz Ferdinand and the Ting Tings. It drew a number of young Hollywood stars to this desert city southeast of Palm Springs.