Two of James Braid's five Claret Jugs were won at the Home of Golf but not since the last of those in 1910 has a Scottish golfer triumphed on the famous Old Course.
Not much about Montgomerie's form in the build-up to The 134th Open suggested he would be the man to change that record and when crunch time arrived, Montgomerie's start was ominous. His opening drive of the Championship ran through the notoriously wide first fairway and trickled into the Swilcan burn.
A bogey put him immediately on the back foot but the Scot had contested enough Opens to know golf's original Major is a marathon, not a sprint - and after recovering to post a 71 on day one, he moved through the pack in style on one of the most memorable Fridays in Championship history.
Much of the attention centred around Jack Nicklaus, who was bringing the curtain down on an incredible professional career, allowing Montgomerie to slip under the radar.
The withdrawal of David Toms meant Montgomerie was playing in a two-ball alongside a compatriot in Paul Lawrie who had won The Open in front of a home crowd at Carnoustie six years earlier.
By the end of his round, a stunning six-under-par 66, Monty had given himself a real chance of following in Lawrie's footsteps.
"Being a two-ball, we were having to wait around and, on the 12th, we sat down for a good half hour until the photos [of Nicklaus] had all been done," Montgomerie recalled.
"It was a strange feeling. It felt like we weren't playing in The Open, we were just having a two-ball. I'd known Paul for many years and we just played a round of golf."
Montgomerie's performance set up a Saturday to savour, with the Scot up to second and therefore going out in the final group alongside Tiger Woods.
"I couldn't believe the support," he said. "Woods normally gets the crowd behind him - he was the world's favourite golfer at the time.
"But not in Scotland on that Saturday. For the first time in my life, I was. The Scottish flags flying, the Union Jacks - it was quite incredible."
The atmosphere rose down the front nine and a birdie at the 10th pulled Montgomerie to within a shot of his American rival.
Woods' mastery of tricky conditions came to the fore thereafter, however, as he kept Montgomerie at arm's length - though a superb birdie at 18 completed a round of 70 for the home favourite, one better than Woods on the day.
"I'll never forget the roar," he said. "The whole town around that amphitheatre on the 18th is quite unique in every way.
"My 70 to his 71 was something I'll always take away."
Hopes of a fairytale triumph were raised again on the final day, which Montgomerie began in the penultimate group, three shots adrift of the lead.
An eagle putt at the ninth gave him the opportunity of drawing level with Woods on -13 and, though it fell short, Montgomerie tapped home for a birdie that kept him firmly in contention.
Yet a bogey on the 10th, then another on 13, all but ended his chances as Woods closed out his second Open victory at the same venue as his first five years previously.
The fading of Montgomerie's challenge did little to dampen the hero's welcome that greeted him on the 18th green as he closed out a level-par 72, leaving him -9 for the week.
It was the fourth of five runner-up finishes in Montgomerie's Major career and his best-ever finish at The Open, creating memories to last a lifetime.
"I'll never forget The Open Championship of 2005," he said. "I'll take that to my dying day.
"I loved the support and I thank them to this day for trying to get me over the line."