The Suffolk side got off to a flying start before repelling any danger possessed by the visitors, who improved after the break but could do nothing about the 2-0 margin.
Buoyed by three straight wins, Ipswich almost scored with just one minute and 24 seconds on the clock.
Jonathan Parr’s deep cross was met first time by a volley from Murphy but former Town stopper Scott Loach clawed the ball away at his near post.
It did not take long for the deadlock to be broken after Luke Chambers’ header was pushed down, rather than away, by Loach and Murphy headed home the rebound.
Rotherham were shell-shocked and Loach was quickly picking the ball out of his net again after McGoldrick picked up Luke Hyam’s short pass and beautifully found the corner of the net with a 25-yard left-foot strike.
The visitors had little in reply, with Alex Revell shooting wide from distance on 16 minutes and Parr blocking Joe Skarz’s goalbound effort shortly after.
Ipswich were oozing confidence but they still owed a massive debt to skipper Chambers, who bravely threw himself at Ryan Hall’s shot on the half-hour mark before Skarz’s shot flew wide of the far post.
The visitors continued to carve out half-chances, with Jordan Bowery meeting Ben Pringle’s cross with a firm header but Dean Gerken standing firm.
Back came Ipswich and Paul Anderson’s deft centre was met at the far post by Christophe Berra, who drew a save from Loach low at his near post.
The Rotherham man remained the busier of the two keepers and he showed smart reflexes to deny Chambers’ diving header soon after.
Just before the break, McGoldrick was just unable to firmly meet Tyrone Mings’ dangerous cross before Anderson skewed a shot wide after he wrong-footed two floundering opponents.
Within two minutes of the restart, it should have been three after Frazer Richardson’s poor back header was seized upon by Conor Sammon, who rounded Loach but hit the foot of the post.
At the other end, Paul Green could not direct a header beyond Gerken before Chambers again came to Ipswich’s rescue to deflect Lee Frecklington’s shot which was heading for the bottom corner.
Rotherham were refusing to give in and Frecklington saw another shot deflected away, this time by Mings, with the visitors in the ascendancy.
To their credit, Rotherham bossed the possession and shots stats and they almost pulled a goal back with eight minutes to go when Gerken saved Green’s deflected free-kick but Richardson fired the rebound well over.