Faldo withdrew after 12 holes because of an elbow injury. He tweaked a torn capsule in his left elbow when he made a gesture during a putt on No. 6. The six-time major champion was on the 13th tee at 1 over when he shook hands with playing partners Kenny Perry and Tom Kite and walked off the course.
"I really wanted to play. I was all geared up," said Faldo, whose only other Champions Tour starts came in the Senior Open Championship. "I want to play good golf, but I can't play with one arm."
Nelson played the first nine holes in 6-under 29. He won the last of his 19 Champions Tour titles in 2004.
The 54-year-old Cochran, the 2010 winner, had an eagle and five birdies for a back-nine 30.
Defending champion Bernhard Langer was a stroke back along with Kirk Triplett, Mike Goodes, Michael Allen and David Frost. Triplett is coming off a successful title defense two weeks ago in the First Tee Open at Pebble Beach.
Kenny Perry opened with a 68. The Charles Schwab Cup points leader, Perry won the Senior Players Championship and U.S. Senior Open in consecutive tour starts this summer. He won the 2011 event for his first Champions Tour title.