The 28-year-old from Inverness finished on six-under-par 282, only three shots behind the winner, Scott Stallings, at the Farmers Insurance Open at Torrey Pines in San Diego.
At one point Knox was only a shot off the lead during the final round but vital birdies eluded him over the inward half.
Knox has now topped $1m in earnings on the Web.com Tour and the PGA Tour, and that does not take into account the money he made on the satellite tours after he turned pro following four successful years on the American college circuit while at Jacksonville University.
Knox said he was very pleased with the start he has made to I am very pleased with my start to the yerar. "I am becoming more comfortable on the PGA Tour and starting to really believe in my talent," he said. "I am focusing more on what makes me play great golf and not worrying about anybody else. I'm very excited about the rest of the year."
Knox said he would like to come home to play in the Scottish Open at Royal Aberdeen this summer.
"If I have secured my PGA Tour card by that point in the season, I would love to play in the Scottish Open. I played Balgownie in the Scottish Strokeplay when I was an amateur and I did pretty well, if I remember. It's a great links course."
Knox lies 45th on the PGA Tour money list with $243,101.