Luiten had seven birdies in a bogey-free round in the morning at Dom Pedro Victoria Golf Course, and Coetzee matched him in the afternoon after starting with six birdies in his first eight holes.
''I'm very happy, 7-under, no bogeys, seven birdies - that's what you want every day,'' said Luiten, who missed three cuts in his last four tournaments. ''I knew my game wasn't far off and the good thing about golf is there's always next week. This week it feels nice.''
Coetzee had an impressive start and posted a 30 at the turn, but ended with a bogey and two birdies in his final nine holes.
''I read an article yesterday about 59-watch and after eight holes I was thinking, 'OK, if I birdie the next one and the next one and the next one...,''' he said. ''I guess I shot myself in the foot a little bit today but I was quite happy with the way things went.''
Coetzee missed four cuts in a row before finishing in a tie for third last week at the KLM Open.
''I've always played well around this track, posted some good finishes and I really enjoy the golf course,'' Coetzee said. ''It suits my eye pretty well.''
Defending champion Padraig Harrington shot 4-under 67 to finish in a tie for 16th.