Appleby is one shot ahead of Jerry Smith and D.A. Points, who shot matching 67s to share second place at minus-5.
Darren Clarke shot a 4-under 68 as well, but then withdrew from the tournament to fly home to be with his wife, who is battling breast cancer.
A release issued by the PGA stated that Clarke withdrew after 'receiving results from ongoing medical tests of his wife Heather' and returned to his home outside London 'to discuss further treatment with Heather and her doctors.'
Vijay Singh, the two-time defending champion and a three-time Houston Open winner, leads a group of 13 players who share ninth place at minus-3.
The only member of golf's 'Big Five' entered into the field this week, Singh mixed five birdies with two bogeys in his first round.
In all, there are 74 players even-par or better after the first round. They are all looking up at Appleby.
Taking advantage of good scoring conditions in the morning, Appleby collected seven birdies with just one bogey to take the lead.
'Conditions were quite easy this morning, no wind blowing, so if you weren't too intimidated by pins being sort of four yards from the edges you could go at a lot of them,' Appleby said.
Appleby birdied three holes on the front nine, reaching red numbers first after he knocked a wedge within 3 feet at the par-4 third.
At the sixth, Appleby pulled a putter on the fringe and rolled in a 25-footer for a birdie. He then two-putted from 60 feet at the par-5 eighth for his third birdie.
Appleby carded back-to-back birdies from the 10th, reaching 5 under with a 25-foot putt at the 11th. His second shot on 13 found the hazard, leading to his only bogey of the day.
On the 17th, Appleby chipped in for another birdie, then rolled in a 20-foot putt at the last to finish off his 66.
'I think that there was definitely a 6 under score to be had out there by somebody,' said Appleby, 'and I was fortunate enough where my round wasn't clean and perfect but there was enough shots where I hit it good enough to give myself opportunities.'
Appleby owns the first round lead for the sixth time in his career. He finished outside the top 10 each of the last two times he held at least a share of the 18-hole lead, including at last year's PGA Championship.
'Could have been better, but could have also not chipped in and made some other stuff,' Appleby said of his round Thursday. 'Otherwise a very good solid start. I sort of like the way my game feels right now. I think the course will fit a lot of players' eye this week.'