The standard between the two former world champions was far from impressive, but Murphy held himself together after a strangely subdued Higgins had missed a blue on 51 in the final frame having looked likely to clear up.
"John wasn't at his best, but he is so hard to beat. That is what makes him a great," said Murphy. "I might have to change my nickname from magician to Houdini after that win. I keep getting out of these tight spots. It is first to six not four, and Mark Selby came back from a bigger deficit last night.
"I always had a chance because it was best of 11 rather than nine frames. I'm a bit of a snooker fan, and I have watched so many of the greats produce under pressure over the years.
"When that moment comes, they have to step up to the mark. I said to myself walking to the table, 'come on, let us see what you've got'. Fortunately tonight it was there."
Murphy's reward is a meeting with defending champion Neil Robertson in the last four on Saturday afternoon. It is a repeat of last year's final that Australia's Robertson won 10-6.
Robertson made three centuries on his way to a thrilling 6-5 win over Mark Allen earlier on Thursday.
"Neil is playing the best of anybody in the tournament," added Murphy. "It was a phenomenal standard today. He is a great, great player and nothing but the best will do against him."
Murphy opened the match with a knock of 85 to lead 1-0 after Higgins somehow flicked a white into a baulk pocket off the brown in trying to pot a red.
But the four-time world champion Higgins would proceed to take the next three frames despite playing a few gears below his very best.
He levelled proceedings with 49 and 53 in the second frame before the match descended into a scrap in the next two frames with Higgins doing marginally enough to outlast his opponent.
Murphy had several chances to win the third frame, but refused a tricky brown after slotting green with the rest.
Higgins would mop up brown, blue, pink and black to lead 2-1. A similar effort saw him sink the required colours for a 3-1 advantage after a safety duel.
That quickly became 4-1 as Higgins constructed what would be his highest break of the night with a 69 to leave himself two frames short of the winning line.
Murphy's response was immediate as he gained access to the table with a long red before running in 70 to trail 4-2.
Murphy made 40 in the seventh frame before somehow knocking the black off the table in his attempt to pot it.
Higgins saw a double attempt on a brown narrowly fail to drop - that would have set him up for a 5-2 lead - but Murphy returned to slot brown, blue and pink to trail 4-3.
The mood of the match was changing as an error by Higgins at the outset of the eighth frame saw Murphy piece together 77 to level at 4-4.
Murphy was first among the balls in the ninth frame, but Higgins was handed a reprieve to move one frame up with a possible two frames to play aided by a 61.
Higgins should have claimed the 10th frame, but he missed a straight red on the cusp of victory holding a 49-36 lead with only three reds left up as Murphy compiled enough points to force the deciding frame that he would win.
Wishaw's Higgins looked in a state of disbelief afterwards having run out of position seconds after scattering the reds for what looked like a match-winning contribution. But he left himself a difficult blue that he jawed to a centre pocket.
"It is a tough one to take," said Higgins. "I threw it away. Full credit to Shaun for the way he has cleared up in the final frame, but the standard of the match wasn't great.
"I was leading 4-1, but I have to say that I threw it away."
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