Former England under-21 international goalkeeper Murray was making his first appearance at Molineux in 19 months after a long battle to recover from a foot injury.
But he made light of that as he frustrated Ipswich Town with a first-half penalty save and a stunning 52nd minute stop to ensure that Jim Magilton's side remain pointless after the opening two games of the season.
Jay Bothroyd's first goal for Wolves in the 27th minute proved to be their match winner but they made hard work of holding on to their advantage.
They had to play for the final 53 minutes with 10 men after striker Carl Cort saw red when he foolishly pushed Gavin Williams to the floor.
Ipswich should really have made their manpower advantage pay - especially when they won a 45th minute penalty only for Murray to save Matt Richards' spot-kick.
When Dean Bowditch then had a 52nd minute goal disallowed for offside, Magilton must have known it would not be his night.
Coming hard on the heels of last Saturday's 2-1 defeat at home to Crystal Palace, it has not been the start to his managerial career that Magilton had been hoping for.
But for Wolves, with four points from two games, it has been as good a start as they could have hoped for after a summer of upheaval.
Bothroyd broke the deadlock in some style but he should really have pounced after just two minutes only to shoot weakly at Shane Supple.
Rohan Ricketts and Jamie Clapham also wasted clear chances before Bothroyd came up with a moment of magic.
Ricketts made amends for his earlier miss by winning the ball and setting up Bothroyd who fired an unstoppable left-foot shot beyond Supple from 25 yards.
But their dominance was undone when Cort needlessly saw red for pushing out at Williams as they tussled for the ball on the halfway line.
Predictably, Ipswich were revived by having an extra man to call on and they should have hauled themselves back on level terms in first-half stoppage time.
Nicky Forster neatly turned away from Jody Craddock before being sent crashing to the floor by the Wolves' skipper.
Referee Trevor Kettle had no hesitation in pointing to the spot before Murray spared Craddock's blushes with a stunning save to beat out Richards' spot-kick.
Williams, who drove on Ipswich from midfield, then saw his 52nd minute shot tipped on to the post by Murray before the loose ball was turned home by Bowditch - only to be frustrated by the assistant referee's flag which summed up their evening.
Wolves: Matthew Murray, Jamie Clapham, Gary Breen, Jody Craddock, Lee Naylor (Seyi George Olofinjana 49), Kevin O'Connor, Mark Clyde (Rob Edwards 45), Karl Henry, Rohan Ricketts, Carl Cort, Jay Bothroyd (Craig Davies 64)
Subs not used: Leon Clarke, Michael Oakes
Sent off: Carl Cort 36
Ipswich Town: Shane Supple, Jason De Vos, Daniel Harding, Luis Castro Sito, Alex Bruce, Richard Naylor, Matthew Richards (Darren Currie 62), Jaime Peters (Sam Parkin 86), Dean Bowditch (Alan Lee 53), Gavin Williams, Nicky Forster
Subs not used: Lewis Price, Fabian Wilnis
Booked: Alex Bruce 14, Gavin Williams 90, Darren Currie 70
Attendance: 19199