Oct 1 (Reuters) - Twice winner Tyrrell Hatton overcame three bogeys on a frustrating back nine to card a two-under 70 and take a one-shot lead in the Alfred Dunhill Links Championship second round on Friday. The Englishman started the day at eight-under and looked in control with two early birdies before tough windy conditions saw him bogey the 10th, 13th and 16th holes at Kingsbarns, ending the day on 10-under for the tournament. Compatriot Daniel Gavins sank an eagle on the par-five 14th to move into second place with a four-under 68 at Carnoustie, while former Masters champion Danny Willett made the most of a lightning start -- two birdies and an eagle in his first three holes -- to stand two shots back following a round of 69. The championship is being held across three courses in rotation over the opening three days -- the Old Course at St Andrews, Carnoustie and Kingsbarns -- with the final round to be played at St Andrews. Tommy Fleetwood, who played alongside Hatton in Europe"s Ryder Cup defeat at Whistling Straits last week, carded a one-under 71 that tied him for fifth at seven-under. Irishman Shane Lowry was four shots off the pace after a solid round of five-under 67.