The trio of Kate French, Samantha Murray and Mhairi Spence got the ball rolling by successfully defending the title won by Murray, Spence and Heather Fell in Rome last year.
But the good times didn't stop there, with double Olympian Woodbridge, ranked 22nd in the world, winning Britain's first individual men's World Championships medal for 20 years as he collected silver.
Woodbridge's season has been blighted by injury and after arriving in Chinese Taipei with his best performance being a 16th at the Rio World Cup in March, the 27-year-old admitted he was struggling to comprehend his success.
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"It hasn't really sunk in yet, but it feels good," said Woodbridge. "I've had a difficult year so it’s nice to finish on a high.
"I've had a couple of injuries that have prevented me getting the results I wanted and I think I needed this. Winning silver at the World Championships is by far my best result.
"I feel like I've worked hard for this for so many years, but I've just missed out for different reasons in the past.
"The shooting was really important and I knew if I nailed that I would be in with a chance. I was in the zone in the shooting and I only missed two shots."
There were also strong performances by two younger athletes, with French tenth in the women's individual competition and Jamie Cooke fifth in the men's.
Elsewhere, Murray was 14th, Freyja Prentice one place further back and Spence finished 17th in the women's event,
And Jan Bartu, pentathlon GB performance director, said: "What a day! It’s been a really tough competition for the girls, but they proved they’re the best team in the world by winning the World Championships team title in consecutive years and the Europeans this year.
"Kate French deserves recognition. She has worked hard in her first full senior year, a year in which she also graduated from the University of Bath, so finishing in the top-ten at this level is a fantastic achievement and is very promising to for the future.
"Ahead of the championships I was looking for a couple of top-ten finishes, so to have three top-ten finishes, a team gold and an individual silver already says everything.
"A men's individual medal has been 20 years in the waiting, so what Nick has done is fantastic."
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