Mark Adair pointed a replica pistol at Helen Baillie as she was getting ready to close Menstrie Filling Station on 28 December last year.
The 32-year-old entered the shop wearing a balaclava and escaped with Â£100 from the till.
He denied the charges, but was found guilty at the High Court in Edinburgh. Sentence was deferred.
Adair's distinctive red Honda Civic was caught on CCTV travelling to Menstrie and driving away from the Clackmannanshire village following the raid.
Ms Baillie told the court Adair had pointed a black handgun, which appeared to be real, at her and demanded money and the keys to the safe.
She said: "He told me to get the keys or he was going to shoot me. I kept saying I didn't know how to do it.
"He pointed the gun at me and said to me that he knew where I stayed, he knew where my family stayed and he was coming back to shoot me."
A jury took less than an hour to find Adair guilty of assaulting and robbing Ms Baillie. He was also convicted of possessing an imitation firearm.
Lord Jones deferred sentence until next month for background reports.
Police launched a "long and thorough investigation" into the robbery, titled Operation Torres, and arrested Adair at the end of January.
Det Ch Insp Jim Smith said the probe had utilised resources from across Police Scotland.
He said: "By committing this brazen crime, Adair put his victim through an appalling experience.
"He showed no regard for her wellbeing, and used an imitation weapon to purposefully frighten.
"Thankfully crimes of this nature remain rare but when do occur, Police Scotland will not be tolerate them and we will use all our resources to bring those responsible to justice."
A masked raider who threatened to shoot a petrol station worker has been convicted of assault and robbery.