John Henderson struck and then ran over Audrey Gray shortly after he had been at a Rangers match in May last year.
Despite the 50-year-old lying dying on the road, Henderson fled the scene and didn't call for help.
He told a jury that the death was a tragic accident after his vehicle "lurched" forward while he was trying to adjust his car seat.
Henderson insisted: "I am a careful and competent driver."
But, he now faces jail after he was convicted at the High Court in Glasgow of causing death by dangerous driving.
Henderson showed no emotion as he had his bail continued until sentencing next month.
Lord Justice Clerk Lord Carloway deferred sentencing until August 20 at the High Court in Edinburgh.