"If I had really putted well today it could have been very low," Schwartzel said. "The good thing is that I know it's there. It very easily could have been low but it was still a solid round of golf and this is still a tough golf course."
Finch and Riu also put themselves into contention with 5-under 67s, with Finch also avoiding any dropped shots and adding five birdies. Riu had six birdies and just a single drop on No. 18.
Frenchman Romain Wattel is fourth on 9 under and Denmark's Soren Hansen fifth on 8 under.
South African Hennie Otto second behind Madsen in the new 2014 Race to Dubai standings is tied for sixth with England's Ross Fisher on 7 under, five back from Schwartzel.
PGA Tour regular Brendon de Jonge is making steady progress and up to a tie for eighth on 6 under with a 68.
Early money list leader Madsen had a disastrous third round after sharing the halfway lead with Schwartzel. The Dane had four bogeys going out and three bogeys and a double bogey coming home, and only two birdies.