McDowell's round tied the course record at the St. Andrews Old Course.
McDowell, who won the Italian Open this year, missed a birdie put on the final hole that would have given him a record-breaking 61.
"I was walking up to the green with my caddie, and I said to him, 'I saw this putt a million times on television and I know exactly where it's going,'" McDowell said. "But it turned more than I expected."
Aaron Carter is still in love with Hilary Duff
Ray Liotta sues skin care company over use of likeness