GB scored three times on the powerplay while netminders Nicole Jackson and Ella Howard both contributed towards the shutout.
Kirk scored his sixth and seventh goals of the group stage to go one ahead of Gregory Hofmann who was on target for the Swiss.
For GB, playing its sixth game in nine days, this felt like a challenge too far. Despite another brave goaltending performance, this time from understudy Jackson Whistle, the Czechs dominated much of the play and finished with 46 shots on goal against 19 from the Brits.
Liam Kirk scored his fifth goal of the World Championship to go one clear at the top of the goalscoring charts – and Matthew Myers was named captain for the game on the special occasion of his 100th GB cap.
Liam Kirk scored twice to take his tally to the tournament to four, while Ben Davies and Mike Hammond were also on target on another famous night for British ice hockey.
Ben O’Connor scored his 18th international goal and Mike Hammond was also on target, scoring late to take the game to the extra period