Iain Steel is one stroke behind the leaders after a round of 5-under-par 67. Jess Daley, Sean Murphy and Ryan Palmer are tied one stroke further back at minus-4.
Barcelo opened his round with a birdie on the second hole at Midland Country Club. The 28-year-old then rolled home back-to-back birdies from the fourth to climb to minus-3.
'It is amazing that when you like the golf course, you tend to play better,' Barcelo said. 'I certainly like this golf course. It is fair, tough and the greens are pure.'
He came back with a birdie on the par-4 ninth. Around the turn, Barcelo moved to 5 under with a birdie on the par-5 12th and capped his round with his fourth birdie of the day on the par-5s, this one coming on No. 15.
'It was a combination of my putting coming around when my ball striking was suspect and vice versa,' said Barcelo. 'Overall, I'm happy with shooting 6 under.'
Jordan playing one group behind Barcelo also opened with a birdie on the par-5 second. He also came back with a birdie on the par-4 fourth.
The 39-year-old Jordan birdied the par-4 seventh, but stumbled to a bogey at the following hole. He climbed back to 3 under with a birdie on the ninth. Jordan ran off four straight pars before converting back-to-back birdies from the 14th.
He closed out his round with a birdie on the par-4 17th to tie Barcelo atop the leaderboard.
'I hit my irons well, drove it well and made some putts,' Jordan said. 'The fairways are narrow here. It is nice to play a course where the shorter hitters have a chance even though the course is over 7,300 yard long.'
Jason Dufner, who won the Gila River Classic last week, opened with a 3-under-par 69. He is joined there by Virginia Beach Open winner Michael Long, as well as Scott Gump, Bob Heintz, Mark Hensby, Jim Benepe, David Branshaw, Keoke Cotner, Ryan Howison, Edward Loar, Casey Martin, Patrick Moore, Sonny Skinner and Mike Standly.
Tag Ridings, the defending champion, opened his title defense with a 2-under-par 70, where he is tied for 22nd place.