Murray, who claimed Olympic silver at London 2012 last summer, has a 48-point advantage in first place after two events in Chinese Taipei with the effects of Typhoon Trami leading to the postponement of the competition at that stage.
After hours of heavy rain, the ride and combined run-shoot were postponed due to the safety of the athletes and horses and will now be run on Saturday along with the men's final, which sees Brits Jamie Cooke and Nick Woodbridge compete.
Murray won 21 of her 34 fencing bouts and posted the fastest 200m freestyle swimming time of 2:10.58minutes for the lead with defending champion and fellow Brit Mhairi Spence tenth, Freyja Prentice 15th and Kate French 18th.
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With Murray, Spence and French's efforts counting towards the women's team competition, Britain are in the lead in that too ahead of Ukraine and China and GB Pentathlon performance director Bartu is in an optimistic mood.
The British team train at the Pentathlon GB high performance centre at the University of Bath and Bartu said: "It's gone fine for us up to this point, but it's not over yet. I really enjoyed the intensity of all four girls' performances in the fencing.
"They really did themselves justice after a hard year, and they each managed to finish on a really positive note. That should give them confidence that will hopefully remain with them overnight."
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