Hodges finished with a 24-under par total of 260 at TPC Twin Cities, where he'd pushed his lead to as many as seven and seen it shrink to three over playing partner J.T. Poston before Poston's disastrous triple-bogey at the final hole.
That left Poston, who carded a two-under 69, tied for second with Kevin Streelman and Scotland's Martin Laird. Streelman carded a 66 while Laird produced a seven-under-par 64 that featured five birdies and a 20-foot eagle at 18.
None of them ever really looked like catching Hodges, who started the day with a five-shot lead.
He pushed that to seven after a birdie at the second and an 11-foot eagle at the par-five sixth.
After a bogey at the ninth he eagled the par-five 12th in spectacular style, landing his 257-yard second shot within three feet of the pin.
Hodges responded to a three-putt bogey at 15 with another birdie at 16, and answered a bogey at 17 -- that saw his lead reduced to three shots -- with a final birdie at the 72nd hole.
He could enjoy the congratulations of the crowd as he walked to the 18th green having stuck his third shot from the fairway a foot from the cup.
"It's been a dream week," said the 28-year-old ranked 110th in the world, who won for the first time in his 65th tour start.
Poston had looked a sure bet for solo second, arriving at the tough par-five 18th three strokes behind Hodges but three clear of Laird and Streelman.
His tee shot landed in the right rough, narrowly avoiding the water hazard. From an awkward stance on the bank he opted to go for the green rather than laying up but his ball ended up in the lake.
"At the end of the day it's not the way I wanted to end, but I had to try and give it a shot and see if there was some way I could make three there at the end and put some pressure on Lee," Poston said. "It was a shot that was going to be hard to pull off, but we weren't playing for second place."
Dylan Wu and Keith Mitchell shared fifth on 268. Defending champion Tony Finau was a further shot back alongside Sam Ryder and Aaron Baddeley.
Beau Hossler matched the TPC Twin Cities course record with a career-low 62 that featured eight straight birdies from the ninth through the 16th.
That had put Hossler in a tie for fourth as Hodges and Poston teed off.
"Usually, you shoot that kind of number on Sunday and you ideally have a chance to win," he said.
