That left Scott well behind long-hitting American Dustin Johnson, who reeled off five birdies in a flawless 65 to take control of the prestigious PGA Tour event won five times by golfing great and Fort Worth resident Ben Hogan.
"I thought I actually hit plenty of good shots and played from the fairway for four over, so it wasn't ideal," Scott told reporters about his start after teeing off at the par-four 10th.
"But I managed to tighten up on the back (nine) and make a couple of putts."
Scott, just the second Australian to become number one following Greg Norman's final reign which ended in 1998, bogeyed the 11th, 15th, 17th and 18th as he limped to the turn.
However he then upped a few gears, reaching the green in two at the par-five first and two-putting for birdie before picking up another shot at the par-four second where his approach ended up three feet from the hole.
"All of a sudden, I had the momentum going the way I wanted and I managed to hang on for the next few holes," Scott smiled. "It's a testing golf course. I just have to be a little patient.
"Sometimes on a course like this, you need to be. Even with a short iron or a wedge in your hand, you can't force it because bogeys are easy to come by."
HIGH-PROFILE COMPANY
Scott played the opening round in high-profile company, twice Colonial champion Zach Johnson carding a 70 and his fellow American Jimmy Walker, the FedExCup points leader, returning a 67.
"It was a fun day," said Walker, who has triumphed a season-high three times on the 2013-14 PGA Tour. "There was a good vibe in the whole group. It was very calm and mellow."
Dustin Johnson, who clinched his eighth career win on the PGA Tour at the WGC-HSBC Champions in November, birdied four of his first nine holes as he surged to the top of the leaderboard.
However, he was given a helping hand late in the day by compatriot Hunter Mahan, who had been one ahead before double-bogeying the last for a 66 to finish level with Americans Robert Streb and Harris English, and New Zealander Tim Wilkinson.
Among those knotted on 67 with Walker were PGA Championship winner Jason Dufner and 2013 PGA Tour rookie of the year Jordan Spieth, a native Texan.
American Boo Weekley, who won last year's title to get his name engraved on the Wall of Champions by the first tee, opened with a 71.
(Reporting by Mark Lamport-Stokes in Los Angeles; Editing by Frank Pingue)
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