Woodland led by one shot overnight after Hojgaard, chasing his first PGA Tour win, backed up a sublime eight-under-par 62 on Friday with a seven-under-par 63 on Saturday.
But the American showed remarkable calm and control on a masterful front nine, featuring four birdies, to move into a lead he never looked like relinquishing.
Hojgaard also had two bogeys and one double bogey, despite two birdies, in his first 10 holes to boost Woodland’s chances.
The Dane closed the gap to five shots on the 14th hole – finding a birdie while Woodland carded a bogey – then four shots with another birdie on the 16th.
But Woodland matched him with a par on 17 and another par at the last, while Hojgaard dropped another shot.
Woodland received a warm reception from the crowd down the stretch, which turned to rapturous applause and chants of “Gary, Gary” as he sank his putt for victory.
It is Woodland’s fifth PGA Tour triumph and perhaps sets him up to challenge at the first major of the season at next month’s Masters.
When asked about his chances at Augusta, he emphasised he still had personal and mental issues to work on, but added: “My game is better than it’s ever been.”
American Johnny Keefer and Australia’s Min Woo Lee tied for third, one stroke behind Hojgaard, on 15 under.
Reflecting on his achievement, Woodland said he was “most proud” that he “didn’t give up” on his career over a difficult past few years.
He added: “I tried to slow down and take things in because it didn’t feel like this was possible a couple of years ago.”