The 26-year-old six-time European Tour winner shot a three-under 68 on the final day to feature among a three-way tie for fourth spot.
It followed scores of 71, 64 and 68 in the competition’s first three days and made him the best-placed Briton this year at Hilton Head.
PGA Tour veteran Stewart Cink finished 19-under and four shots clear in South Carolina to comfortably clinch his third RBC Heritage title.
The 47-year-old, who previously won at Hilton Head in 2000 and 2004, went into the final round with a five-stroke lead on the back of a 54-hole record-score of 18-under 195.
Danny Willett finished 10 shots back from Cink on nine-under after he carded scores of 68, 71, 67 and 69.
Speaking to reporters after his win, Cink said: “It was just a really good, solid week all the way through.”
