The Scottish No 1 closed with a four-under-par 67 for a seven-under 277 total on the Sea Pines course at the South Carolina resort.
He finished two shots behind South African Grace (66) alongside former Scottish Open champion Luke Donald (71), with American Bryson DeChambeau (68) sharing fourth spot on his pro debut.
“I’ve been playing well the last three days, so I knew I had the potential to shoot a good round and today I played a great,” said Knox afterwards. “I was thrilled with the way I putted this week, especially after the first day.
“The last three days I’m proud of myself. I put in some time practising and actually figured out how to make a few.
“I was thinking if I shot three under par on the back nine I might have a chance, so I was happy with the way I conducted myself and the shots I hit coming down the last few holes.”
It was the 30-year-old’s best performance since winning the WGC-HSBC Champions in China last November then losing in a play-off in the OHL Classic at Mayakoba in Mexico the following week.
“The conditions this week were extremely difficult, but I love playing in the wind,” he added. “This course is tough, but it’s perfect for me. It’s one of my favourite courses. I expected to play well.”
He is up to third in the FedEx Cup behind Adam Scott and Jason Day and has climbed 11 places to 29th in the world rankings. Knox has also jumped up to 29th on the world points list in the Ryder Cup standings, having gone into the latest PGA Tour event sitting 66th.
His WGC win didn’t count in the battle to make Clarke’s team for the match at Hazeltine in September. However, Knox is now a European Tour member and is determined to get in the mix as the scramble for spots reaches the business end in the summer.
“Winning again would mean the goal of playing the Ryder Cup, but I am just so fortunate to be playing in these great tournaments like the majors, the WGCs and being a member of the European Tour,” he added. “I have just to soak it all in and go for it.”
Next up for Knox might be the Players’ Championship, after which he is heading back across the Atlantic for the Irish Open at The K Club then the BMW PGA Championship at Wentworth. “I might take a few weeks off right now,” he said. “It will be nice to put my feet up on the couch.”
For Grace, it was his breakthrough win on the PGA Tour and follows his successful title defence in the Qatar Masters earlier this year. “This really puts the cherry on top of the cake,” said the 27-year-old. “And I’m excited for things to start. I can tick this one off the box and head into the next couple of majors trying to win it. I have one notch, I’ve done it before and I can do it again.”