Murphy will face defending champion Mark Selby or four-times world champion John Higgins in the last four on Saturday afternoon at London's Alexandra Palace.
Murphy lamented cold conditions around the main table in the arena a day after Neil Robertson berated the sweaty nature of surroundings at the North London venue during his 6-5 win over Mark Allen.
"I was really annoyed at the start because there was cold air coming into the arena which affected the way the table was playing," said the 2005 world champion.
"The temperatures make such a difference to the way the tables play, and how the balls react on the table.
"If there is a slight difference, it can make us look very silly. I don't know what to sound as if I'm making excuses. There like was an Arctic wind coming across from the air conditioning trying to make it cooler than yesterday, but it had a massively adverse effect on conditions until they (World Snooker) turned it off. They turned it off later on, and I thought the tables played better.
"It has been a long time since I played so well in the arena. It is nice to see it still there.
"I've never given up in matches."
Murphy was thrilled to win on his mum Jean's birthday. He continues to oversee an impressive record at Alexandra Palace since the invitational tournament moved away from Wembley Arena in 2011.
He lost to Neil Robertson in the final two years ago before losing to Australia's number one in the semi-finals 12 months ago.
Murphy was happy enough to sign an autograph for an eager supporter despite falling 3-0 behind.
"You see golfers doing it during round," commented Murphy. "You'll never see me refusing an autograph. The fans are all that matters. We don't have a sport without them."
Fu opened with a 76 after Murphy failed to pick out a long red.
Murphy looked well placed to draw level, but missing a black off its spot on a 48 break enabled Fu to clear the final pink for a 2-0 lead.
Murphy had chances in a messy third frame, but he could not prevent Fu from snaring it.
It was imperative that Murphy stopped the bleeding, and did so with a run of 49 helping him register his first frame of the match to trail 3-1.
The first two frames after the mid-session were split with Fu - from Happy Valley in Hong Kong - running in 71 to lead 4-1 before an 86 from Murphy saw him recover to trail 4-2.
Murphy would follow that up with a knock of 81 to move within one frame of his opponent before Murphy pounced on a bad Fu miss on a red to make 117 in restoring parity at 4-4.
Fu looked to be in command of the ninth frame when he moved 18 points ahead on the colours with Murphy twice failing to hit the yellow from a tough snooker.
Fu opted against potting the yellow twice when it looked the right shot to play.
It was to prove the wrong decision with Murphy polishing off the colours to pinch a fourth straight frame on the black. "I would have taken the yellow on on any other day, but today my long potting was terrible," conceded Fu. "I was losing my timing on the long potting..that's why I didn't take it on. I just didn't fancy it. At the end, I played a poor safety shot. I have no excuses. Shaun potted a long yellow. That was a very important frame."
Fu's game continued to descend into a state of torpor as he missed two simple reds before Murphy ran in 64 to seal a rousing win.
Fu last played in the Masters when he lost the 2011 final to Ding Junhui, but says he was never comfortable with his form.
"Leading 4-1, I wasn't playing great," commented Fu. "I didn't really turn up today.
It is nice to be back again after a three-year absence. Is is a great honour.
"I think either Ronnie (O'Sullivan) or Mark (Selby) are still the favourites to win the tournament, but it will be tough."