While Faxon was rewarded for making the effort to travel from the United States with a 64, Rafferty was disqualified for failing to return his scorecard at Lundin.
Ulsterman Rafferty, the former European No 1, hit two balls out of bounds on the 17th to run up a quintuple-bogey nine and felt enough was enough when he also sent his approach to the 18th out of bounds and decided not to finish the hole.
Two hours later, Faxon played the 17th, a par-four of 345 yards, in six strokes less, courtesy of a three, one of seven birdies in his flawless round which was just one short of the course record.
Faxon was eligible to play in the qualifying event in America but insisted he could not break a commitment to host a charity event at the same time in Rhode Island.
Unlike some of his fellow Americans, Faxon was determined to play in The Open and entered final qualifying for the first time since 2000 - when he missed out at Lundin. "It was a good day's work and a pretty stress-free round," said Faxon. "The course was there for the taking, but I know it will take another of those to get me into St Andrews."
Qualification this year is tough with 384 players fighting it out for 12 places - three from each of four courses
Sweden's Per-Ulrik Johansson carded a 70 at Ladybank while another former Ryder Cup player, Hampshire's Steven Richardson, shot a 68 at Leven Links.
Durham's Robert Dinwiddie celebrated his Walker Cup call-up with a three-under-par 68 at Ladybank. Dinwiddie was named in the Great Britain and Ireland men's amateur squad who will attempt to win an unprecedented fourth straight victory over the United States in Chicago in August, and now has an excellent chance of playing at St Andrews as well. The 22-year-old from Barnard Castle recently graduated from Tennessee State University as the top-ranked English collegiate player and won the Scottish and Welsh Amateur strokeplay titles in the space of seven days last month.
Dinwiddie, who smashed the amateur course record at Alwoodley with a 65 in regional qualifying last Monday, said: "I played fairly steady. It would have been nice to go lower but with a low one [today] I'll have a chance."Reuse content