The British quartet headed reigning European champions Italy by 2.59 seconds.
Among the British quartet were three Rio 2016 Olympic Games champions, including Laura Kenny, who has returned to the team after missing the 2017 European Championships because of her pregnancy.
In 2017, Great Britain lost to Italy in the final, but Kenny can be the decisive factor this time around, as Italian rising star Elisa Balsamo pointed out.
""They are much stronger now," she said. "They have Kenny back after her pregnancy so it's even tougher for us.
"Everybody knows they're really strong, a very solid team. They won many Olympic medals so we all know they are like that."
In Friday's women's team pursuit first round, Italy will face Germany, while Great Britain will be up against France.
Italy headed the men's team pursuit qualifying, led by their latest addition, Olympic omnium champion Elia Viviani.
Surprisingly, current world champions Great Britain advanced to the next round only in fourth place, the last spot available.
"It was a bit disappointing to be honest," Ethan Hayter (GBR) said. "We have been going quite well in training so we expected to be a little bit quicker but that's racing, you can't count on anything before it's happened."
In Friday men's team pursuit first round, Italy face Great Britain, while Switzerland take on France.