Appleby said the course would yield low scores if the wind stayed down -- and it did throughout his round.
"Conditions were quite easy," Appleby said. "There was definitely a 6-under score to be had out there by somebody and I was fortunate."
The breeze picked up later in the day, though, and the course toughened up.
"The wind can kind of mess with you a little bit," said John Daly, who shot a 69 in the afternoon. "It can change on your backswing."
Appleby said his round wasn't "clean and perfect," but a couple of "bonus" shots led to the sparkling score.
He sank a 25-foot birdie putt on the sixth and another on No. 11. He hit a bad approach to the par-5 13th for his only bogey, then chipped in on No. 17 and made a downhill 20-foot birdie putt on the 18th.
"I hit it good enough to give myself opportunities," he said. "Could have been better, but could have also not chipped in and made some other stuff."
Appleby won the Houston Open in 1999, when it was played at the TPC at The Woodlands. Aussies have fared well at the event, winning five other times.
The other Australian-born Houston champions David Graham (1983), Bruce Crampton (1975 and 1973) and Bruce Devlin (1972).
"I think it's about the wind and breeze. It's a little bit like Australia," Appleby said of Houston.
Jerry Smith and D.A. Points also benefited from early tee times and shot 67s.
Smith, who turns 42 on Monday, is back on the PGA Tour for the first time since 2002.
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