The 46-year-old Northern Irishman fired five birdies in the opening 12 holes at the tour's flagship event before dropping his first shot of the day at the short 14th.
Clarke, however, took advantage of the closing par-fives with two birdie fours securing a two-under final aggregate of 286.
"It's been coming but it's the first time I've taken it on to the course for a while," he said.
Clarke was named 2016 Ryder Cup captain in February, succeeding Irishman Paul McGinley, but his form has been scratchy since his appointment.
His best finish on the European Tour this season was a tie for 15th at the Tshwane Open in South Africa in March.
Clarke will have extra incentive to do well with his home crowd behind him when he tees up on Thursday in the Irish Open first round at Royal County Down, a tournament hosted by world number one Rory McIlroy.
Among the other leading players taking part next week are Rickie Fowler, Sergio Garcia, Padraig Harrington, Graeme McDowell, Lee Westwood, Ernie Els, Luke Donald and Martin Kaymer.
(editing by Justin Palmer)
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