Horsey rallied after making double-bogey on the 12th hole with an eagle on the 17th and then par on the final hole to finish level with McGrane at 13-under 275 at the end of regulation.
The Englishman then two-putted for par on the 18th hole in the playoff, while McGrane found a greenside bunker and took a bogey.
McGrane made seven birdies in the final round, but failed to close out his first victory in six years in his round of 66.
It was the second time in Horsey's career that he has been in a playoff and the second time he's come out in front after winning the 2011 Hassan 11 Trophy at Agadir, Morocco, in similar fashion.
"It's a big relief to win and very much like my last win in Morocco when I also made a mess of a couple of holes on the back nine," said Horsey. "But standing on 17 I really didn't know where I was in the tournament so after hitting my ball through to the back of the green I realized I was three behind and needed to do something drastic and quite quickly.
"So chipping-in for eagle was a great help and then thought I needed to make birdie at the last but not realizing Damien (McGrane) had dropped one there at the last."
Horsey led after the opening two rounds and went into the final round tied for the lead.
"To win is very special as it's been a while since I won in Morocco, and also it's been bumpy road along the way since then," he said.