Matty Lee, 19 from Leeds, and Lois Toulson, 17, from Huddersfield, claimed a silver medal in the mixed 10m platform in Hungary.
Toulson and Lee moved up from sixth into the medal placings with a run of consistent dives.
The teenagers combined to score 323.28 points as China’s Ren Qian and Lian Junjie took gold with 352.98.
“We feel really good right now,” said Lee.
“China are so strong and it’s tough to beat them, but we knew we just had to keep calm and focus on ourselves. It feels so great to win that silver medal.”
Toulson added: “It was amazing to win that silver in this competition. We are a really good partnership, we both train in the same place and we are really good friends which really helps.”
After Lee and Toulson’s heroics, attention turned to Laugher and Mears.
The Leeds divers won Britain’s first Olympic diving gold in Rio last August, but fell short of the podium on this occasion.
Russia’s Ilia Zakharov and Evgenii Kuznetsov took gold with 450.30 points, with China’s Xie Siyi and Cao Yuan second and Ukraine’s Oleg Kolodiy and Illya Kvasha third.
The British pair were more than 11 points adrift of the podium. Laugher and Mears had been aiming to add the world title to their success at the European Championships, Commonwealth Games and Olympics.
Laugher said: “Finishing fourth sucks. We are disappointed.”
Mears, who has been battling against a back problem, added: “Preparations weren’t perfect and you always have niggles, but today is a bit of heartache because we really wanted to medal at this event.”
Harrogate’s Laugher, 22, is set to compete again next week in the individual 3m springboard event.