Despite dropping the first set Venus and Klaasen came out firing at the start of the second.
They forced a deciding point in Murray's opening service game after Venus had held serve to take a 2-0 lead.
But Klaasen dropped his next service game on a double fault after Soares had set up the break point opportunity with a return of service winner.
Venus and Klaasen created a break point in the ninth game on the Soares serve but Murray came up with a superb volley to stave off the danger.
Soares then hit two wonderful return of service winners off the Venus serve to bring up a deciding point in the next game but a huge first serve got the Kiwi and South African out of trouble.
Murray then served two double faults to hand Venus and Klaasen two set points and Klaasen hit a lovely return of serve to break and take the set 6-4 to force a deciding match tie break.
Murray and Soares raced to a 4-1 lead but the Brazilian lost his net two service points to keep Venus and Klaasen in it.
But Venus dropped his next two service points and the fourth seeds went on to win the match tie break 10-4.
The round robin format means Venus and Klaasen are still very much in the running to make the semifinals.
They have two more matches, against second seeds Juan Sebastian Cabal and Robert Farah of Colombia, and seventh seeded Croatian Nikola Mektic and Austrian Alexander Peya.
The top two teams in each group advance to the semifinals.
Last year Venus and American Ryan Harrison won their three round robin matches before losing in the semifinals.
It's a lucrative end to the season for Venus who has so far earned US$543,000 ($806,110) in prize money after reaching the Wimbledon final and final of the Toronto Masters 1000 tournament.
Each pair earn US$100,000 as an appearance fee in London with US$38,000 for each round robin win.
A semifinal match win would earn US$103,000 and US$200,000 for winning the final.