An out-of-sorts Murray, who was playing his third rubber of the weekend following Saturday's doubles victory alongside brother Jamie, looked to be in trouble as he trailed Simon by a set and a break.
Simon had two medical timeouts during the match following heavy falls and Murray, a double grand slam winner, was able to capitalise in front of partisan crowd at the sun-kissed Queen's Club in west London.
The gritty Frenchman was able to continue despite the falls but was severely limited in his movement and could only chase gingerly as Murray moved him around the court with his pounding groundstrokes and delicate dropshots.
Murray completely dominated the final set and sealed the victory when Simon skewed a backhand wide.
"Obviously it feels unbelievable to get through that, it wasn't looking great," Murray, who jumped around on court and punched the air before sitting with his head in his hands, told the BBC.
"The whole weekend has been fantastic. This team has done amazing things, we're punching above our weight here and we're now in the semi-finals of the biggest team competition in tennis.
"I'm just proud to be in this position and I hope we can do well in September."
Britain will play Australia in the semi-finals after they recovered from a 2-0 deficit to win 3-2 against Kazakhstan.
"It should be a great match," Murray added. "Australia have some top young players and (Lleyton) Hewitt who has a lot of experience. It will be fun and hopefully there'll be another good atmosphere."
(Reporting By Tom Hayward, editing by Pritha Sarkar)
Share
