* Rose first golf winner for 112 years * UK player wins in dramatic finale By Liana B. Baker and Andrew Downie RIO DE JANEIRO, Aug 14 (Reuters) - Britain's Justin Rose birdied the final hole to win the Olympic golf tournament on Sunday, the first gold medallist in a sport that returned to the Olympics in Rio after a 112-year absence. Rose, who scored a hole in one on his first day, carded a final round four-under-par 67 to beat Henrik Stenson by two strokes in a competition that went all the way to the final putts. The overnight leader was neck-and-neck with Stenson throughout much of the round but he hit a lovely approach shot to within feet of the pin at the final hole. More...