There has not been a home winner in Scotland on the European Tour since Paul Lawrie won the Johnnie Walker Championship in 2012 in Gleneagles, but Forrest and Hill improved the prospects after climbing to 18 down in Fairmont St Andrews.
Forrest starts the day seven shots behind the overnight leader Lucas Bjerregaard and his chance to challenge at the top of the standings seems far away from an opening bogey.
But he responds with a brilliant birdie that turns around the corner, which he continues on the back nine, to match the track record of 62 – determined by Denmark Bjerregaard in the second round – to take the lead of the clubhouse.
Hill started strong and took a two-stroke lead early in the round, but Forrest’s birdie run saw his compatriot with two shots with four holes to play after bogeys on the 10th and 14th.
Hill, who was born less than 40 miles from the track, regained his composure with birds on the 15th and 18th to join his compatriot at the summit, along with the other Scots. David Law in the vicinity at 16 below.
Hill had the second birdie, just as playmate Bjerregaard conceded the same hole to put at the top of the standings.
An eagle at the next Hill extended his lead to two when Bjerregaard picked up a shot and the Scot climbed to 18 down to birdies on the sixth and seventh.
Forrest, after an opening bogey, made his move with a win on the third before taking six straight birdies out of the sixth. He missed another birdie on the 12th, but again a shot on the next.
Hill dropped to 16 under after dropping his first two shots of the week, while Forrest was alone at the summit after wins on the 15th and 16th.
He briefly extended the lead to two shots with his 11th birdie of the day, but Hill got him down at 18 with late wins.
Spaniard Santiago Tarrio is the closest rival of the Scottish duo at 17 under, with Law and two-time European Tour winner Bjerregaard one shot further back.