Lafeber shot a two-under 69. He earned a spot in next week's British Open because he was the lowest finisher not otherwise eligible.
Ian Poulter had 65-268 to take fourth place.
Clark closed with a birdie that enable him to tie Tom Lehman's 1997 tournament record.
"I really did want to make that putt on the last," admitted Clark, who tied for third at this year's U.S. Open. "I didn't want to have to make one for par there, so it was great to see that go in."
Clark got his third European Tour win, his second this season. He won the South African Open earlier this year and in 2002.
Notable deaths of 2014 [PHOTOS]