The 22-year-old, who began the tournament as the third lowest-ranked player in the field at number 48, had never won a match on his two previous visits to the Crucible but is now in the quarter-finals.
Higgins, the 1998 world champion, had looked in control when leading 4-1 on Saturday night but his opponent strung together five consecutive frames to move 6-4 ahead and then sustained his terrific form.
Entering the concluding session 9-7 up, Murphy allowed the fifth seed only one more frame and clinched the biggest success of his career by rattling in a brilliant 115 break.
“That’s the best anyone has ever played against me here, including Ronnie O’Sullivan when he beat me in the final four years ago,” said a shell-shocked Higgins.
Another high-profile casualty was Jimmy White, who gave his fans one last hurrah before he was sent tumbling out by Matthew Stevens.
‘The Whirlwind’ went into the concluding session 12-4 down, with his opponent needing only one more frame to secure a quarter-final match against Stephen Hendry.
And the Welshman was made to wait 25 minutes to wrap up his victory as the six times World Championship runner-up made the scoreline look slightly more respectable by knocking in a winning break of 68.
But a missed long green early in frame 18 proved to be White’s final shot of the tournament, Stevens compiling a 69 to complete a 13-5 success having done the damage by winning seven out of eight last night.
“In a way there was quite a bit of pressure on me today because I wanted to get it over with as quickly as possible,” said the Welshman, who was beaten in the final by compatriot Mark Williams five years ago.
“Jimmy had beaten me the last couple of times we played, but I felt confident going into the match and was really up for it.”
Maximum man Mark Williams is out after a last frame defeat to Ian McCulloch.
The Welshman, who completed his opening victory over Robert Milkins with a perfect 147 break, led 5-3 at the end of the first session but lost six frames when the match resumed to trail 9-7 going into last night’s finale. Williams got it back to 12-12 but McCulloch held his nerve to win the decider.
Peter Ebdon, the 2002 champion, fought back from 6-2 down to tie his ‘grudge’ match against Stephen Lee at 8-8.
The contest contains added spice because of the last time they clashed at this stage, Ebdon infuriated Lee with his celebration after a 13-12 win.