Oliver, who missed last year's Olympics after a wretched time with injury, had been the form athlete all year and ran impressively throughout the competition in Moscow.
He led early in the final and maintained his form to take an emotional victory in 13.00 seconds, the fastest time of the season.
American dreams of a clean sweep came up just short as veteran Ryan Wilson took silver in 13.13 but a last-hurdle stumble by defending champion Jason Richardson allowed Russia's Sergey Shubenkov to snatch bronze in 13.24.
Olympic champion and world record holder Aries Merritt ran a ragged race and could finish only sixth.
"You know how hard it is to win a title, it's my first one and after a couple of years with some injuries it feels good," the 31-year-old Oliver, who came to Moscow as the world leader with 13.04 seconds, told reporters.
"After the disappointment of not making the Olympics I had to re-set. I had to change my training, my weight rules - I knew that this was the year and if it didn't happen this year it was going to be very tough," he added.
"I feel as if I've been running consistently all year - maybe not the 12s of a few years ago but 13-flat was enough to win the gold tonight."
With Merritt struggling early in the season nobody had gone under the 13-second mark and the openness of the event seemed to be underlined by Wilson's unexpected victory in the U.S. trials.
However, the 32-year-old journeyman, who has had wretched luck with injuries when big events loomed, showed it was no fluke with a great run for silver.
"They stuck me out in lane nine - nobody thought I could do this," he said.
"Maybe next year if I win the trials they won't be surprised."
Shubenkov gave the sparse Luzhniki Stadium crowd something to cheer when he came through for bronze as Richardson caught the last barrier and lost all momentum, ending U.S. hopes of a first global clean sweep in the race since the 1960 Olympics.
Merritt's run illustrated how quickly things can change at the top level of sport. Last year he won Olympic gold and smashed the world record, but a hamstring injury suffered in May left him off the pace all summer.
He had something of a lucky escape in the semi-finals earlier on Monday after being left for dead in the blocks.
Merritt scraped into the final with a pedestrian 13.44 after local favourite Konstantin Shabanov pulled up injured and Jamaica's Hansie Parchment, Olympic bronze medallist last year and second-fastest this season, caught the penultimate barrier when going well.
Oliver, meanwhile, advanced comfortably and the big man, who has spent much of the year being asked about Merritt's performances, can now sit back and talk about his own.
"I've worked so hard for it, made so many sacrifices," Oliver said. "It feels so great to finally hang this thing around my neck."