McDowell, winner of the 2010 U.S. Open, carded a one-under-par 70 while Sterne returned a 71 as the pair ended on five-under 208.
Austrian Bernd Wiesberger (68), David Howell of Britain (69) and Australia's Richard Green (70) shared third place on 209 while Dane Thomas Bjorn (74) was two strokes further back despite twice finding water off the tee on the back nine.
"It's going to be phenomenal come 2018," McDowell told reporters. "The last four holes are as dramatic a risk-reward finish as you could imagine with a combination of a natural amphitheatre.
"The 15th and 18th are two phenomenal holes especially the pin position on 15 today. When the caddie in the group in front put the pin back in the hole I thought he'd missed the green with it - it looked like it was in the water."
World Match Play champion McDowell and Joburg Open winner Sterne are both aiming to record their second European Tour victories of the season.
McDowell has had a bizarre sequence of recent results. The Ryder Cup stalwart, who also won the U.S. Tour's RBC Heritage event in South Carolina in April, has either won or missed the cut in his last seven tournaments.
"I'm very pleased with my 71," said Sterne. "This course can bite you in a lot of places and the finish here is probably the toughest on the tour.
"There are a lot of guys bunched up. Someone can come from further back but hopefully I get off to a good start again tomorrow and keep it going."
Also in title contention on 210 are Briton Simon Dyson and Dane Soren Kjeldsen while Bjorn is one of eight players on 211.
(Writing by Tony Jimenez; editing by Alison Wildey)