The South African was two over after five holes on day one at Emirates Golf Club but fought back to get himself within two of the lead after three rounds and in with a good chance of claiming a fourth European Tour victory.
Three bogeys on the front nine on Sunday sent him tumbling down the leaderboard but Stone never gave up and came home in 34 to finish at 13 under after a 72, four shots behind winner Paul Casey.
"It felt horrible," he said of his front nine. "Felt like I was doing a couple of rounds with Mike Tyson.
"Felt like I couldn't get the ball on the green, to be fair. Felt like I was putting from a distance and every time I was putting I was putting for par.
"The long walk from nine green to the tenth tee box kind of reset everything. I kind of just said, 'all you have to do is hit one good shot and one good shot'. Got very fortunate on ten to get a good bounce and get on the green and two putt for birdie and the momentum kept on building.
It felt horrible. Felt like I was doing a couple of rounds with Mike Tyson
"To finish level par in the conditions that we had and all the pressure is something I'm very proud of."
He added: "Any time you're going to be in contention here at the Emirates, it's quite special. The media have been supporting this tournament for many years, and the illustrious list of winners that have their name on the trophy is quite special.
"On top of all that, I got to play with Sergio (Garcia) which is like a boyhood dream come true.
"I think I played solid golf last week in Abu Dhabi, a rough patch of five holes on Friday morning but other than that, it's been very steady, very solid golf.
"It's definitely something to build on and something to help motivate me for the weeks to come and at the moment, as good as this week has been, I'm focusing on Saudi next week and maybe try and grab one or two places better."