Second seed Murray twice fell behind in the second set but recovered both breaks immediately to eke out a 1-6, 7-6(7-4), 6-2 victory and stretch a winning streak against his French opponent to 12 matches.
"In all the matches so far this week, I have not started very well," the world number seven told reporters, conceding he did not know what was to blame for his tardy openings.
"I lost my first service game in every match and that has not helped because my opponents have gained confidence and played very good tennis.
"It's not easy starting every match from behind. I managed to turn the game at the end of the second set, started to play a little bit better. I was making sure I was not making so many unforced errors," the Scot added.
"I found a way to win the match even though I was feeling I was not playing my best tennis. I'm glad that I managed to do that.
"Maybe I just try and warm-up better, maybe practice a little bit closer to the matches."
Murray's semi-finals opponent will be Grigor Dimitrov, who needed two hours and 40 minutes to battle past Ernests Gulbis 4-6, 7-6(7-2), 7-5 in the final quarter-final match of the day on Cancha Central.
An injury to his left abductor muscle denied Ferrer a chance of registering a fifth straight final appearance.
The three-time champion won the first set 6-2 but was 4-2 down in the second when he retired against South African fifth seed Kevin Anderson, who moves on to face Ukraine's Alexandr Dolgopolov in the last four.
Image: Andy Murray of Great Britain.
Photograph: Cameron Spencer/Getty Images
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