Grace produced the day's moment of magic – a drive to five feet on the par four 16th, setting up a decisive eagle as he shot a round of 66 for a 19 under par total.
The win was Grace's second of 2015, having already captured the Alfred Dunhill Championship in South Africa.
The day started with both Grace and Warren in a four-way tie for the lead with Emiliano Grillo and Bernd Wiesberger, but more players also mounted challenges on a dramatic last day.
Warren started well when he birdied the first from ten feet and second from 15 feet, but then double bogeyed the short eighth to see his charge falter.
Wiesberger started badly by bogeying the second and third, but had birdie efforts at the fifth and seventh and headed for home with three straight gains to take control of the tournament.
France's Grégory Bourdy shot a 6-under 30, but his title bid ended when he failed to get up-and-down on the 15th hole.
Korea's Byeong-hun An also shot 65 and narrowly missed a birdie on the last hole.
Warren recovered with birdies at the ninth and tenth, while Grace went ten holes without a birdie before holing from ten feet at the 12th.
Grace's moment of magic at 16 looked to have been enough, but Warren birdied there and holed an eight footer at the short next after a brilliant tee shot, but could not match Grace's birdie at the last after the South African pitched to three feet.
Warren's 67 saw him finish alone in second on 18-under, with Wiesberger third after a 68 and Eddie Pepperell's inward 32 giving him solo fourth after a 67. An, Bourdy and Grillo were tied for fifth on 15-under.