Stenson, chasing his first European Tour win in three and a half years and a spot at next week’s DP World Tour Championship, picked up a shot at the second while his nearest challenger and playing partner Merrick Bremner responded with a birdie at the next hole.
However, the Dubai resident's four shot advantage over Coetzee was quickly trimmed to two in a matter of moments as both players ensured contrasting fortunes in the sand.
The Swede landed his tee shot into a fairway bunker on the fourth and was only able to hack into the rough en route to a bogey.
Meanwhile Coetzee continued to thrive after the turn as, despite driving the green on the par fourth tenth, he landed his shot from the sand within a within feet off the hole to record yet another birdie.
Although Coetzee and Bremner sat in the upper reaches of the leaderboard, compatriot Charl Schwartzel slipped back and looked unlikely to become the third successive winner to originate from the Rainbow Nation.
Schwartzel three-putted at the fourth for a double bogey before he dropped two more shots at the sixth after a wayward tee shot.
Englishman Tommy Fleetwood turned in 35 despite a pair of bogeys as he targets the high finish which could secure his place on the 2013 European Tour International Schedule.
Fleetwood, who came into this event ranked 124th, with the top 119 retaining their playing privileges for next season, was six under for the tournament after the front nine.