Graham, who created history in last year’s Scottish Amateur Championship by becoming the youngest player to reach the finals at just 14, finished second in one of the biggest events on the amateur calendar after producing a brilliant last-day performance at The Open venue.
The title eventually fell to England’s John Gough, but he needed a timely birdie-3 at the 17th to edge ahead of Graham after the mop-haired young Scot had set the clubhouse target with a closing one-under 69.
Graham, the world No 669 but a far better player than that indicates, had opened with two 71s on Friday and Saturday before stepping up his challenge with a 70 in the penultimate round on Sunday morning.
He dropped a shot at the fifth in the final circuit before rallying with birdies at the seventh, eighth and 11th. After a bogey at the 17th, he signed off with a 69 to finish on one-over 281.
Gough, the younger brother of 2019 Walker Cup player Connor, found himself tied with Graham after dropping three shots in a row on the back nine before regaining his composure to make a title-winning birdie-3 at the 17th.
Still in the amateur ranks, Scottish champion Chloe Goadby (St Regulus) finished in a tie for second behind England’s Alice Barlow in the Welsh Women's Open Stroke Play at Southerndown.
Goadby, who watched boyfriend Laird Shepherd play in last month’s Masters at Augusta National, carded rounds of 73-75-73 for a one-under total, four behind Bury St Edmunds player Barlow.
On the Ladies European Tour, Michele Thomson recorded her third top-10 finish of the season by securing a share of fourth spot behind Swede Maja Stark in the NSW Women’s Open at Coolangatta & Tweed Heads Golf Club.
Thomson started the final round with a triple-bogey 8 before also dropping shots at the second and fourth, but, in a gutsy fightback, the Aberdonian made six birdies in seven holes around the turn.
The impressive salvo saw her sign off with a par-72 to finish on eight-under and, on the back of her effort, Thomson now sits eighth in the season-long Race to Costa del Sol.
Stark finished five shots clear of the field as the 22-year-old claimed a third LET win in eight months. “I am super happy,” said one of the circuit’s new rising stars.
It was a disappointing final day for the Scottish contingent in the DP World Tour’s Catalunya Championship, won by home player Adri Arnaus at the sixth extra hole in a play-off with South African Oliver Bekker.
Chasing a second win in three starts after his breakthrough in the Qatar Masters in March, Ewen Ferguson ended up joint-52nd after dropping 40 spots on the back of a closing 78.
The Glaswegian finished on one-over alongside David Drysdale (75), one behind David Law (73) and one ahead of Grant Forrest (71).
In the opening round of matches in the Scottish Area Team Championship, title holders Lothians beat North 6-3 at Bathgate while Borders also made home advantage count at Peebles, where Fife fell 5.5-3.5.
Host club player Jack Mann won on the Scottish Junior Tour at Fortrose & Rosemarkie, closing with a 67 for a two-under 211 total, finishing two shots ahead of Kemnay’s Fraser Laird, with the girls’ leaderboard being topped by Northampton’s Jade Potter on 228.