McGoldrick marked his return to the side by giving the home team the lead in first-half stoppage time.
Mathias Ranegie spurned a decent opening for Millwall when he headed over the bar from Scott Malone's good delivery on 23 minutes.
Paul Anderson was denied on 28 minutes when met a cross from Chris Parr, but the former Liverpool midfielder's effort was well saved by David Forde in the Millwall goal.
Anderson went close again five minutes later when he fired wide from the edge of the box after McGoldrick had teed his teammate up.
After the break, Scott McDonald forced Dean Gerken into an smart stop with a free kick, before Murphy doubled Ipswich's lead just after the hour mark.
The striker took full advantage to fire home from close range to give the Tractor Boys the points in East Anglia.