Murray silenced the doubters who claimed he was distracted by dreams of Davis Cup glory with a gritty 6-4, 6-4 win over David Ferrer, while Nadal, beset by problems during the worst year of his career, showed he isn't finished yet with a 6-3, 6-2 thrashing of French Open champion Stan Wawrinka.
Former Wimbledon champion Murray has made it clear his main priority in the closing weeks of the season is Great Britain's attempt to win the Davis Cup for the first time since 1936 in their first final since 1978.
Britain face Belgium in the final on clay in Ghent next week and Murray had initially suggested he might pull out of the Tour Finals to fine-tune his preparations for the Davis Cup.