It seemed as though Higgins was coasting through the deciding frame as he built a 51-0 lead, but when he missed a tricky blue Murphy took his unexpected chance with a brilliant 66 break to earn a 6-5 win.
Higgins would wonder how he lost a match in which he had led 4-1 and 5-4 as he shook hands with his fellow former world champion.
Scotland's four-time Crucible champion has won two Masters titles but it has not been a tournament that has brought him consistent success, exemplified by his 10 first-round defeats.
Earlier, Robertson reckoned he played the shot of his life to set up a match-winning century as the defending champion edged out Mark Allen.
Robertson's made an amazing escape form an Allen snooker and from there the Australian made a classy 105 to win the match 6-5.
Allen, however, labelled Robertson's shot a "fluke".
Nevin leads Lionhearts
BOXING: Mullingar man John Joe Nevin outclassed fellow Olympic silver medallist Daouda Sow to help the British Lionhearts to a home win over the USA Knockouts in the World Series of Boxing (WSB) clash in London.
Nevin took all five rounds to earn a unanimous (49-46,49-46, 50-45) decision over the French lightweight, a finalist at Beijing 2008, at York Hall.
Nevin's win stretched the Lionhearts' advantage over the Americans to 2-0 following Kaupo Arro's triumph over Jeffrey Camp in the opening fight of the five-bout Group B match.
Wales' Andrew Selby then fired the Lionhearts into an unassailable 3-0 with victory over Ireland's Michael Conlan, a bronze medal winner at London 2012. Selby claimed a unanimous decision from a cracking five-rounder.
2014 Tour goes English
Cycling: The 2014 Tour de France will visit the English cities of York, Sheffield and Cambridge, after the county of Yorkshire hosts the 'Grand Depart', Tour director Christian Prudhomme said.
The July 5 start will be followed by stage two between York and Sheffield.
After visiting London on day three the Tour then returns to mainland Europe.
NBA: Detroit 87 NY Knicks 102, Minnesota 77 LA Clippers 90, Phoenix 94 Milwaukee 98,LA Lakers 90 Miami 99.