Murphy's clinical shot off the underside of the bar broke the deadlock in the 62nd minute before substitute Paul Anderson capped a fine cameo display with a decisive second in injury time.
It was no more than Ipswich deserved after dominating the second half against a Reading side fresh from beating Bolton 7-1 last week.
Both teams shared early chances before, in the ninth minute, only a desperate block from Kaspars Gorkss denied Stephen Hunt his first Ipswich goal after Murphy had headed down Luke Chambers' deep cross.
Reading were then denied a decent shout for a penalty in the 16th minute when Jobi McAnuff went down under Ryan Tunnicliffe's wild challenge but referee Andrew Madley was unmoved.
Two minutes later, the visitors again went close, albeit in fortuitous circumstances, when Christophe Berra headed Garath McCleary's cross against Pavel Pogrebnyak and the rebound went just wide.
It took 40 minutes for the hosts to register a shot on target, predictably from top scorer David McGoldrick, while Reading had their best chance of the half in the 43rd minute when Berra half- clearance only fell to Pogrebnyak but his shot was blocked by a posse of three Town defenders.
That spurred Reading into life and Danny Williams tested Gerken from the edge of the area, the diving Ipswich keeper tipping wide.
A tight first half continued after the interval although Reading goalkeeper Alex McCarthy had to be alert to block Aaron Cresswell's dangerous low cross with his chest as McGoldrick waited to pounce just after the hour mark.
A minute later, Ipswich took the lead. Hunt burst towards the Reading defence before laying the ball across goal to Murphy, via a slight touch by McGoldrick, and the Republic of Ireland striker drove a clinical shot off the underside of the crossbar.
Town should have doubled their advantage with 20 minutes left when sub Anderson picked out McGoldrick with a pinpoint through ball.
McGoldrick did little wrong with his side-foot shot but he was thwarted by the legs of the onrushing McCarthy.
The game was finally opening up and Ipswich left-back Cresswell denied Reading a certain goal with a fantastic goal-line clearance as Nick Blackman waited to touch home after superb work by Jordan Obita.
The visitors were in the ascendancy and Blackman should have tested the Town goal from 12 yards but fired over after his initial shot was blocked.
Ipswich's defensive rearguard impressed before Anderson grabbed a decisive - and deserved - second in injury time, ghosting into the area and beating McCarthy at his near post.