Wiffen hung back for most of his race but snatched the lead from Italy's Gregorio Paltrinieri at the last turn then powered away to win in seven minutes 40.94 seconds.
The Irishman finished more than two seconds better than Australia's runner-up Elijah Winnington, while Paltrinieri, the Olympic silver medallist at the Tokyo Games, faded to third.
Wiffen's triumph came two months after smashing Grant Hackett's 15-year-old, short course world record at the European championships.
Soaking up cheers at the Aspire Dome pool, he made a phone gesture with his hand and slammed it down.
"Obviously the goal coming into this meet was to win a world medal and be on the top podium for Ireland," said the bespectacled swimmer.
"It's Ireland's first-ever medal at a world championship level... It's just really cool to say and I'm really happy."
With last year's world medallists from Fukuoka skipping the women's 200m freestyle, Haughey felt pressure to win the event and ultimately delivered in a time of 1:54.89, nearly a second quicker than New Zealand runner-up Erika Fairweather.
"It means so much to me especially as the past few times, I've just missed out on the podium," Haughey, who won silver in the 100m and 200m freestyle at the Tokyo Olympics, told reporters.
"I'm the first (winner) from Hong Kong but hopefully there's more to come in the future."
Another Tokyo runner-up celebrated a first world title in the men's 200m butterfly.
Japan's Tomoru Honda gritted his teeth through the pain of an ankle injury to win the event in 1:53.88, holding off Italian runner-up Alberto Razzetti and bronze-winner Martin Espernberger.
Honda suffered a fall in the leadup to Doha and said that kicking was painful.
"I was icing my ankle the whole time," he said.
"It was so hard for me but I just told myself: 'Keep moving, keep moving'.
"So happy, I want to say thank you to everyone."
Australian Sam Williamson emerged as a surprise winner in the non-Olympic 50m breaststroke, upstaging a field featuring British world record holder Adam Peaty and the 2023 Fukuoka runner-up, Nic Fink.
Italy's Nicolo Martinenghi took silver, while Fink had bronze. Peaty, who took bronze in the 100m breaststroke on Monday, finished fourth to miss out on a second medal.
In a match-up of second-string relay teams, the United States coasted to a dominant mixed medley gold in 3:40.22 ahead of Australia and third-placed Britain.
China's Pan Zhanle, who set the 100m freestyle world record of 46.80 seconds on Sunday with a stunning lead-off swim in the relay, topped qualifying for the individual final on Thursday with a time of 47.88.
With world champion Kyle Chalmers skipping the meet, along with Fukuoka minor medallists Jack Alexy and Maxime Grousset, Pan is in the box seat to pick up his first individual world title.
American Carson Foster will also bid for his first individual title on Thursday as top seed for the men's 200 medley final.
