Olympics-Golf-Proud Rose wins historic gold medal for Britain

* Rose first golf winner for 112 years * UK player triumphs in dramatic finale (Adds quotes) By Liana B. Baker and Andrew Downie RIO DE JANEIRO, Aug 14 (Reuters) - Britain's Justin Rose birdied the final hole to win the Rio Olympic golf tournament on Sunday, the first gold medallist in a sport returning to the Olympics after a 112-year absence. Rose, who hit a hole in one on his first day, carded a final round four-under-par 67 to beat Sweden's Henrik Stenson by two shots in a competition that went all the way to the final putts. "Honestly this is a dream come true," said Rose. "I've been thinking about Rio for a long, long time. To come out of it with a medal is incredible, and to come out of it with gold, unbelievable. "I was in a great fight with Henrik, a good friend of mine, and it took world class golf to win today so I am very proud of the achievement and I've just got to let it all soak in now." The overnight leader was neck-and-neck with Stenson throughout much of the final round but he hit a lovely approach shot to within feet of the pin at the last hole. Stenson put his long putt past the hole and missed his next shot to card a bogey six. Rose, whose only major victory was the U.S. Open in 2013, birdied and then punched the air and grabbed the British logo on his shirt to the acclaim of the crowd. The United States' Matt Kuchar, who was only included after world number three Jordan Spieth pulled out, finished one stroke behind Stenson to win bronze. Spieth and the other three men in the world's top four - Jason Day of Australia, American Dustin Johnson and Ireland's Rory McIlroy - withdrew from the Olympics, some of them citing concerns over the Zika virus. BACK PROBLEMS Rose and Stenson know each other well from the European Tour and Ryder Cup, where they played one of the most scintillating rounds in the competition's history in 2014, together carding 12 birdies in 16 holes in a four-ball win over Kuchar and Bubba Watson, the U.S. golfers who came third and eighth on Sunday. Stenson said he struggled with back problems over the last few holes and had to have treatment soon after the turn, but he did not make excuses for his silver medal performance that included an opening round of 66 followed by three 68s. "I had a bit of an issue, my thoracic spine kind of locked up completely after 13 holes and I had to have some treatment," said the Swede. "It kind of put me out of my rhythm a little bit but I was still there till the end... "It was going to be a battle today and I think I battled pretty well," he added. "It was kind of head-to-head with Justin all day and it was going to come down to whoever finished the strongest and he birdied the last to win it. "I have no regrets really, I did as well as I could today and congratulations to my good friend who won it today." Few people play golf in Brazil and the par 71 course was built for the Olympics on environmentally sensitive land. It is due to be turned into a public course after the Games, one of just a handful in the South American nation. (Editing by Bill Rigby and Ken Ferris)