McDowell, despite a double bogey at the par-5 14th hole, is at 7-under 137, a stroke ahead of four players in the 12-man field, with two other players at 4-under, after 36 holes.
First-round leader Charl Schwartzel had a 2-over 74 and fell into a tie for ninth, five strokes off the lead.
McDowell opened with a birdie and, after seven pars, just cleared the water protecting the green at the par-5 ninth hole. That allowed him to escape with a birdie. He added three more over his first four holes of the second nine but had trouble getting out of the brush on the 14th and took a 7.
He also had birdies at 16 and 18.
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