Jamie Cooke, Sam Weale and Nick Woodbridge all progressed to maintain a 100 per cent record, all four women having qualified to their final 24 hours earlier.
In addition, Great Britain have already won two medals at the championships – a gold and bronze in the women’s and men's team relays.
“It was an exciting day for us, so far, so good," said British team performance director Jan Bartu.
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“Jamie and Sam went through in a very balanced way and were always in control of their destinies. They were able to conserve some energy for the final, which is good.
“With the complete men's team in the final, it means we have the opportunity to compete in the team event as well, which adds another dimension for us.”
Kate French, Samantha Murray, Mhairi Spence and Freyja Prentice will contest the women's final on Monday - with the first three's scores counting towards the team competition.
GB’s Choong and Cooke finish without a medal in modern pentathlon
GB women end winning run in Olympic modern pentathlon competition