Stewart, a 19-year-old from Harare, produced a superb final dive to total 382.14 points and beat Lan, who registered 375.18pts.
Brian Earley, from the United States, took bronze while the German Borris Lietzow was the one to miss out in the four-man final.
China won four of the six diving titles at the last world championships in 1991 and three of the four at the Barcelona Olympics. The one- metre springboard is not an Olympic event.
They looked set to extend that proud tradition when Lan built a commanding lead over the first four dives. But his last two efforts were poor, while Stewart conjured up a two-and-a-half piked somersault with his last dive.
'I'm incredibly elated. My legs were shaking on the podium because I was so exicted,' Stewart, who is based at the University of Tennessee, said.
No African nation had ever previously won a medal at the world championships, being staged for the seventh time. Stewart picked up a springboard bronze and a three- metre silver at the Commonwealth Games in Canada last month.
China's hopes of a gold medal in the women's 10-metre platform diving event were foiled when a downpour - the first rain in Rome for over two months - forced organisers to suspend the final until today. China's Fu Mingxia is expected to retain the title she won in 1991.Reuse content