The bogey-free effort, which was illuminated by an eagle-2 at the ninth hole at Anahita, gave the 25-year-old from North Berwick a golden chance to secure a top-ten finish in just his second start as a European Tour card holder.
On 10-under, Forrest sits six shots off the lead, held by American Kurt Kitayama and South African Justin Harding.
In contrast, it was a disappointing day for David Drysdale, the other Scot to make the cut. He slumped to a 79 to slip 38 spots, sitting joint 63rd at two over.
Also on the European Tour, Craig Ross continued to give a good account of himself on his pro debut on the circuit in the Australian PGA Championship at RACV Royal Pines Resort in Queensland.
The 24-year-old Glaswegian came home in three-under as he carded a two-under 70 for a three-under total, sitting joint 20th as Cameron Smith stayed on course for a successful defence of the title as he headed into the final round with a three-shot lead.