SAN DIEGO, Calif., June 20 (Reuters) - Spaniard Jon Rahm had one hand on the U.S. Open trophy on Sunday after sinking clutch birdie putts at the final two holes at Torrey Pines in an electric finish to the major championship. Louis Oosthuizen was the only player with a chance of catching Rahm after the other contenders fell away. The South African was one shot behind with three holes left. Earlier, Rahm tied Oosthuizen for the lead when he perfectly judged a sharply-breaking 25-foot (7.6-metre) putt that curled in deliciously for an unlikely birdie at the 17th hole. And his putter stayed hot at the par-five 18th, where he coaxed home a 20-footer on the same green where Tiger Woods famously birdied the last 13 years ago to get into a playoff that he subsequently won. With a 67 -- the only contender not to have a bogey on the back nine -- Rahm picked up his two-month-old baby and walked off to sign for six-under-par 278. He had no choice but to wait to see if it was enough. Back on the course, Oosthuizen after a bogey at the 11th settled down and sank a series of testing par putts to tick off the holes without any damage. He was on the 15th hole when Rahm holed out at the last, and could hardly ignore the ear-splitting roars that greeted the Spaniard"s heroics. Earlier, Bryson DeChambeau and Rory McIlroy were among the big names who came unglued on the most difficult stretch of the course early on the back nine. DeChambeau, who began the final round two shots back, set himself up to become a repeat winner when he nearly made an ace with a wedge at the par-three eighth, his ball stopping an inch shy of dropping in the cup. Still, the tap in birdie was enough to get DeChambeau to two-under on the day and one clear until Oosthuizen, who had a share of the overnight lead, picked up his first birdie of the day at the ninth. But DeChambeau came unglued with a series of wayward drives and poor putts, dropping four shots in four holes to plunge out of contention. McIlroy similarly fell back with a double-bogey at the 12th hole, where his approach shot plugged in a greenside bunker. The final round began with three players, Oosthuizen, American Russell Henley and Canadian MacKenzie Hughes tied for the lead at five under. But as Henley and Hughes faltered, the big boys took over, though not for long for some.