The Canadian duo, undefeated in five international competitions this season, scored 76.98 points to take a four-point lead over Chinese veterans Pang Qing and Tong Jian, who came out of retirement to compete on home ice in their 16th world championships.
Another Chinese pair, Sui Wenjing and Han Cong, were third.
In ice dancing, Madison Chock and Evan Bates will attempt to become just the second American duo to win a world title after taking the lead in the short dance.
Kaitlyn Weaver and Andrew Poje of Canada were second, and defending world champions Anna Cappellini and Luca Lanotte of Italy were third.
Duhamel said she and Radford chose to skate to a song by the French-Canadian singer Ginette Reno because of the luck Reno brought the Montreal Canadiens in the NHL playoffs last year. Reno sang the national anthem before every home game, spurring the Canadiens to victory in the first two rounds.
"As soon as our music starts and we get in that starting position, it brings us back to the familiar feeling of everyday at training and every competition that we've done," she said. "But I have to say, I think before the music started, we were the most nervous we've been all season."
Although the Canadians won the silver medal at the Sochi Olympics last year and are two-time bronze medallists at the worlds, they're not accustomed to coming into a major competition as the heavy favourites.
"We're heading into the long program for the very first time in first place," Radford said. "Having a great skate in the short, of course, helps us feel more relaxed."
Pang and Tong, both 35, first competed at the worlds together in 1999 when several of their current Chinese teammates were just toddlers. The two-time world champions (2006, 2010) and Olympic silver medallists retired after the Sochi Games, but returned to compete in one final worlds.
Tong joked that it wasn't his idea to come out of retirement.
"She wanted to come back, so I followed her," he said.
Now they have a chance to win another gold in front of a boisterous home crowd, though their long program is not nearly as technically difficult as the Canadians, who have a throw quad salchow in their routine.
Chock and Bates, the U.S. champions, scored a career-best 74.47 to top the short dance in ice dancing.
The Americans also led after the short dance at the Four Continents last month before Weaver and Poje came back to edge them for the gold.
"We know we can't rest," Bates said. "We have to absolutely attack the (long) program and skate as though we were coming from behind."
The only other Americans to capture a world ice dancing title were Meryl Davis and Charlie White in 2011 and 2013. The duo hasn't competed since winning the Olympic gold in Sochi last year, but came to Shanghai to skate in the worlds opening ceremonies on Wednesday.
Like Duhamel and Radford in the pairs, Weaver and Poje were the favourites coming into Shanghai having won all five events they competed in this season, including the Grand Prix Finals and Four Continents.
"We've had the weight a little bit this whole season and we put it on ourselves," Weaver said. "Regardless of the result right now, we're so happy with how we've been able to shoulder that pressure and funnel it into the performance."
The women's and men's short programs are on Friday, and the pairs and ice dancing events will conclude with the long programs on Saturday.