South Koreans Noh Seung-Yul (68) and Charlie Wi (71) were tied for third with American John Huh.
Huh shot a five-under 67 which tied for the low round of the day with Matt Kuchar on a day when high winds slowed the pace of play and saw just 19 of the 81 golfers who made the cut break par.
Greg Chalmers (69) was the best placed Australian tied for sixth with Kuchar, Brian Gay (71), Cameron Tringale (76) and David Mathis (77) at three-under.
Curtis had two double bogeys on the front nine, including one on the par-five eighth, where his ball landed on another fairway.
He battled back with three birdies on the back.
Playing in his first career major, Curtis captured the 2003 British Open Championship, emerging victorious as Denmark's Thomas Bjorn surrendered a late lead to finish tied for second with Vijay Singh.
Every made three bogeys but was saved by a couple of birdies, including a 10-footer after a nice tee shot on the par-three third hole.
"Overall, not bad," Every said. "I have a chance to win."
Kuchar got back into contention with a superb round. His only blemish was a bogey on the par-four 11th when the wind took his ball off the green and onto the fringe. Kuchar is the event's top-ranked golfer at 15th in the world.
"I put myself in position," Kuchar said. "Maybe a long shot, but at least a chance."
AFP ash
-AAP
