The red-hot striker is now the Sky Bet Championship’s equal top scorer with nine goals after finding the net in both the 35th and 59th minutes, strikes that sandwiched James Henry’s equaliser.
It was no more than the home side deserved despite a nervy end to the game at Portman Road.
Murphy showed his potency with the game’s first chance as Ipswich took advantage of a slip from Wolves right-back Matt Doherty but visiting goalkeeper Carl Ikeme saved the striker’s powerful shot at his near post.
Murphy then showed his aptitude in defence, getting a last-ditch block to deny a certain goal from Bakary Sako after the Ipswich striker’s initial error.
The home side were just inches away from a 15th-minute opener when Ikeme dropped Kevin Bru’s deep cross but David McGoldrick’s poked shot went just wide.
Ipswich were on top and they came close to scoring a fantastic team goal in the 26th minute.
Jay Tabb, McGoldrick and Bru all combined before Stephen Hunt tucked the ball across goal but the sliding Tabb could not find the required power to beat Ikeme.
Wolves were offering little at the other end although McGoldrick had to be alert to divert Sako’s powerful angled free kick away from his own goal.
The deadlock was finally broken in the 35th minute and in stylish fashion.
Murphy did well to dispossess Kevin McDonald before thinking nothing of shooting early into the far corner for his eighth goal of the season.
It was almost two in the 43rd minute when Tommy Smith rose highest to meet Hunt’s corner but his header was just too high before a neat free-kick ended with McGoldrick shooting tamely at Ikeme.
Out of nothing, Wolves equalised eight minutes after the restart. Henry’s vicious cross missed everyone but deceived Town keeper Bartosz Bialkowski and went in at the far post.
Ipswich looked to respond immediately and Christophe Berra’s goalbound shot was superbly blocked by Danny Batth before Leon Clarke slid a shot just wide at the other end.
And they restored their lead just before the hour mark when Lee Evans’ crossfield pass inexplicably went straight to McGoldrick, who teed up the onrushing Murphy to calmly chip Ikeme for his second.
Matt Doherty just missed the far post with a fizzing effort before Wolves almost conceded a comical own goal when Ethan Ebanks-Landell’s clearance deflected off team-mate Batth.
A frantic ending saw some backs-to-the-wall defending from the home side but they deservedly hung on to claim all three points.