Murray's hopes of ending Britain's 77-year wait for a men's Wimbledon champion were on the verge of being shredded as he found himself playing catch-up while looking jaded and uncomfortable on court.
The 54th-ranked Verdasco put pressure on Murray's vulnerable second serve and came up with a series of rasping winners to force the U.S. Open champion deeper behind the baseline.
Yet with the match slipping out of his grasp, Murray muscled his way back into the encounter, taking the third and fourth sets as Verdasco's level dropped and then grabbed a decisive break in the 11th game of the fifth.
He wrapped up the match after three hours and 27 minutes when Verdasco sent a forehand long.
"There's been a lot of matches where I've been behind and managed to turn it round, I don't know if it is the most emotional match, but it was an unbelievable atmosphere and great to get through," said a hugely relieved Murray, who has now reached five successive Wimbledon semi-finals.
He will face 6-foot-8 Polish beanpole Jerzy Janowicz for a place in Sunday's final.
Murray had reached the final of his last three grand slams, but he found himself under early pressure as Verdasco broke to take the first set after 45 minutes.
That was the first set Murray had dropped all tournament but the world number two shook off the disappointment to take a 3-1 lead in the second.
His tame second serve came back to haunt him, however, and he was broken in the sixth and eighth games. When Murray failed to convert any of the three break points he had in the ninth game, Verdasco surged to a two-set lead.
Faced with a mountain to climb, Murray lost the tightness that had marked the first two sets, breaking twice to take the third comfortably and then edging a close fourth as both players seemed wary of cutting loose.
Yet it was Murray who came out on top in the fifth, rifling down an ace to bring up three match points and then clenching his fist in relief when Verdasco sent a forehand long.
