Horsey had been among among the leaders for much of the competition, but looked to have thrown away the chance to earn his third European Tour title.
A double bogey at the 12th hole of his final round was followed by another dropped shot at 14, while McGrane collected three straight birdies from the 15th to assume pole position.
However, the Irishman then bogeyed the 18th, while Horsey chipped in for an eagle at 17 before parring the final hole to finish level with McGrane on 13 under at Tseleevo Golf and Polo Club.
Horsey then clinched victory with a par at the first extra hole, with his rival paying the price for firing sand with his second shot.
Having led going into the final two days of play, Horsey found himself sharing the lead with Peter Whiteford ahead of Sunday's action.
Whiteford finished fifth at 10 under following a closing 75, with Scott Jamieson and Sam Hutsby carding 69 and 68 respectively to take third and fourth.
McGrane, meanwhile, surged into contention with a wonderful 66 that featured seven birdies prior to his dropped shot at the last.
That slip-up gave Horsey a lifeline and the 29-year-old, who had gone round in 72, capitalised to secure his first win since clinching the Trophee Hassan II in 2011.