The impressive Michael Kightly scored the only goal of the game eight minutes into the second half and the sending off of Gary Breen two minutes later simply seemed to strengthen the resolve of the Wolves defenders to hang on for the three points.
Even the dismissal of Jackie McNamara after 89 minutes failed to provide an opening for the Canaries.
Norwich kicked off attacking the River End goal. In the fourth minute Darren Huckerby opened up the Wolves defence when he picked up Youssef Safri's clearance and headed goalwards.
His charge was halted by a cynical challenge from McNamara, who was shown a yellow card that might easily have been red.
Murray then saved shots from Carl Robinson and Huckerby.
After 31 minutes Huckerby's shot was blocked but fell kindly for Lee Croft who fired wide with the goal at his mercy.
Peter Thorne then got his head to Adam Drury's left-wing cross but the ball dropped over the bar.
Carl Robinson released Huckerby whose trickery and pace took him past the Wolves defence but his shot from an acute angle was turned away for a corner by Murray.
Five minutes from the break Dickson Etuhu looked certain to break the deadlock when he got his foot to Huckerby's low left-wing cross but Murray acrobatically palmed the ball away.
The visitors continued to live dangerously, conceding two more free-kicks that provided shooting opportunities. Murray saved Safri's shot and Etuhu headed over when Safri crossed from the right.
In first-half stoppage time David Marshall made his first save of the game when Kightly got in a long-range shot.
Eight minutes into the second half Kightly beat the offside trap and pulled the ball back for Karl Henry whose shot came back off Marshall's left-hand post.
Kightly was perfectly placed to latch onto the rebound and his right-foot shot from eight yards gave the City keeper no chance.
Breen was then sent off for a professional foul on Huckerby. Safri took the resulting free-kick but it was blocked by the defensive wall.
Murray then saved Huckerby's shot and did equally well when Etuhu tried to chest Huckerby's cross into the goal.
Huckerby did beat Murray ten minutes from time only to see his shot cleared off the line by substitute Rob Edwards.
In stoppage time Jurgen Colin's shot went inches wide and Wolves hung on for a win that owed everything to Murray for his outstanding performance.