The 38-year-old led heading into the final round but a level-par round left him two strokes behind Grace.
Nevertheless, the former world number one was in upbeat mood, saying: "This is a great step in the right direction.
"I am really positive about my game going forward and I am pretty positive about the way I handled it today."
Donald has not had a PGA or European Tour win since the 2013 Dunlop Phoenix in Japan and has now finished second at Hilton Head on four occasions.
Grace was three shots behind Donald by the end of round three, but seven birdies in a 66 propelled the 28-year-old to his first PGA Tour win.
"It's come very quick and I'm just grateful to be in this position," Grace told pgatour.com. "I had to stay patient, I'm stoked."
Scotland's Russell Knox joined Donald in second with a final-day 67.
