Nine under with two holes to play on a vulnerable Augusta National layout, Campbell bogeyed 17 and 18.
That put him a stroke in front of fellow Americans Jim Furyk and Hunter Mahan, who bogeyed the last on a glorious spring day that contained hardly a breath of wind.
While four-times winner Tiger Woods began and ended poorly to shoot a 70 in the favourable conditions, Campbell led a glut of low scores on a course trimmed by 10 yards since last year.
With several tees pushed forward on a layout measuring 7,435 yards, the Texan set a Masters record by starting with five consecutive birdies.
Out in five-under 31, Campbell reeled off four birdies in a row from the 12th before finding a bunker with his approach on 17 and three-putting the 18th green.
A par-par finish would have earned the 34-year-old the 24th 63 recorded in a major.
“I got off on a roll and it’s always nice to make a couple of birdies to start, much less five,” a beaming Campbell told reporters.
“I felt like I was hitting it well all day. Unfortunately I ended up with two bogeys to finish but overall I’m pretty happy with the round. By no means is it easy out there but if you hit good shots you really get rewarded.”
Former U.S. Open champion Furyk was also pleased after carding a flawless six-birdie 66 in the opening major of the season.
“I hit a lot of really good iron shots and kept the ball in play with my driver,” the former world number two said after shooting his lowest round at Augusta in his 13th appearance.
“I made enough putts but I hit a lot of really close shots on that back nine. I had two birdie putts inside three feet and I knocked it pretty close on 16.”
World number one Woods, bidding for his 15th major title, parred the first five holes before running up a bogey at the 180-yard sixth.
