Ice-cool on a hot and humid afternoon at Colonial Country Club, Johnson shrugged off two suspensions in play because of threatening weather to card a sizzling six-under-par 64.
The 2007 US Masters champion broke clear of a congested leaderboard with birdies at 12, 13, 15 and 17 sandwiching a lone bogey on 14 as he posted a tournament record low of 21-under 259.
"There is a reason why I love playing here and I keep coming back," a beaming Johnson said greenside after clinching his seventh PGA Tour title, and his third in Texas.
"The course does suit me as far as shot-making, I think, and certainly the bent grass which is what I grew up on. I just feel honored."
Englishman Davis, who had led by two shots with 11 holes to play in pursuit of a maiden PGA Tour victory, had to settle for second place after bogeying the last for a 68.
Johnson's playing partner Ben Crane rolled in a 32-footer to birdie the 18th for a 67, tying for third at 17-under with fellow American Jeff Overton who also closed with a 67.
For much of the afternoon, it seemed Davis would finally land a breakthrough win just six weeks after he lost a playoff for the Heritage Classic at Hilton Head where he called a two-stroke penalty on himself at the first extra hole.
Co-leader overnight with American Bryce Molder, he birdied the first two holes to edge one ahead before he faltered at the par-four fifth where he had to take a penalty drop after hitting his tee shot into a hazard.
A bogey there briefly dropped him back into a three-way tie for the lead with Molder and Johnson but Davis immediately recovered by rolling in a 12-footer to birdie the sixth.
Having restored his one-shot cushion, the Englishman struck his approach to five feet at the seventh and calmly knocked in the putt to double his lead.
Johnson, however, drew level at the top after making birdies at the 10th and 12th, the second of them a 22-footer which prompted him to pump his right fist in celebration.
He then holed out from a similar distance at the par-three 13th to snatch the outright lead for the first time at 20 under.
Johnson recorded his only bogey of the day at the par-four 14th, finding the right rough off the tee and a greenside bunker with his approach before lipping out from five feet with his par putt.
That left him in a tie for the lead with Davis, who had five holes remaining, when play was suspended for 47 minutes due to the threat of lightning.
Once play resumed, Johnson wasted little time in regaining the lead when he coolly sank a 25-foot birdie putt at the 15th to return to 20-under.
He then knocked in a 14-footer to forge two strokes clear before the siren sounded for a second time to halt the action.
Davis lipped out with a birdie attempt from eight feet at the par-three 17th after play resumed before Johnson comfortably parred the last to secure the title.
