Scott and Day both finished the tournament at two under par after one of the most dramatic final rounds in history on the famous Scottish links.

The pair's 72-hole total of 282 was good enough for top-20 finishes, but not good enough to contend for the Claret Jug with golf heavyweights Tiger Woods, Rory McIlroy, Justin Rose, defending champion Jordan Spieth and ultimately Italian winner Francesco Molinari.

Scott started the last round just four shots off the pace but he floundered with a front-nine 40 before picking up three strokes coming home to join Day in a tie for 17th - six strokes behind Molinari.

The former Masters champion rued a killer double-bogey on the par-4 third after his lob wedge ballooned in the breeze back into the burn and he was unable to get it up and down for bogey.  

"I didn't play very well on the front. Probably most guys struggled on the front. It was very, very difficult," Scott told AAP.

"I'd just want one shot back. My second shot going into the third was such a bad shot.

"Making a double there. I could have easily made a four with one better swing and I would have been satisfied with even par today, considering the way I played.

"I just didn't hit fairways and greens on the front nine.

"I actually scrambled really well and putted really well and got it back, but I wished I'd had another crack at that shot. It was a bad shot."

While Scott lamented his closing two-over 73, Day's three-under 68 - the second-lowest round of the day - came too little too late.

"It's clearly a little bit disappointing to not give myself a shot at even getting into contention," Day said after he was level with Molinari and played with the Italian on Saturday only to enter the final round 10 shots adrift of the leaders and without any real hope.

"But there's a lot of positives from today. It was good to be able to get into the red and beat this course, which was nice."

Australian Open champion Cameron Davis closed with an impressive one-under 70 to finish in the top 40 on his major championship debut.

"He's got all the tools to make it," two-time US Open champion Brooks Koepka said after playing the final round with the 23-year-old Sydneysider.

Lucas Herbert, in his first Open too, dropped three shots on the punishing last two holes for a 77 and four-over 72-hole total, leaving the 22-year-old with a creditable share of 51st spot.

Herbert beat home Marc Leishman, who faded with a 76 to finish at five over in 60th place.

"I didn't have it today," said Leishman, the 2015 runner-up who many tipped pre-tournament as this year's winner.

"Got off to a bad start hitting the first tee shot out of bounds and didn't really get a whole lot better after that, to be honest.

"A disappointing end to the week, but the first three days were promising for the month ahead."

Leishman was one shot - and spot - ahead of Brett Rumford (74), with Cameron Smith's final-round 77 leaving the reigning Australian PGA champion at 10 over and 78th overall.

Australian Associated Press