The Irish striker netted a powerful opener on 32 minutes before his cross was only cleared to substitute David McGoldrick, who coolly doubled the hosts' advantage.
Tim Hoogland set up a nervous finish when his shot was deflected in with four minutes remaining, but Ipswich controlled much of the match and deserved the three points.
Fielding eight debutants, including five in their back line, nervy Fulham conceded a corner after 17 seconds as Ipswich created the early chances through Christophe Berra's powerful header and Luke Hyam shooting just wide.
After 11 minutes, Fulham finally fashioned a decent opening after Scott Parker's exquisite ball played in the marauding Hoogland.
The right-back fed Chris David but he screwed his shot wide after taking up a good position.
Ipswich remained the most likely to open the scoring, Cole Skuse volleying just over with 17 minutes on the clock.
The visitors almost capitalised on an error by Dean Gerken when the Town goalkeeper fumbled David's 20-yard shot but he made amends to deny Moussa Dembele with his legs.
Although Fulham were enjoying the majority of possession, Ipswich continued to create half chances with Skuse again finding space, if not the target, with another dipping volley.
And it was the hosts who broke the deadlock in the 32nd minute when Hyam's incisive through ball released Murphy, who outpaced Shaun Hutchinson before making no mistake with a powerful finish.
Fulham were visibly deflated by the setback but they looked for a quick recovery after the interval and the impressive Konstantinos Stafylidis fizzed a 25-yard shot just over.
Ipswich were looking strong at the back and doubled their advantage at the other end on 62 minutes.
Murphy was again too strong for Hutchinson on the left wing and, while his low cross was half cleared, it fell perfectly for McGoldrick to open his account for the season.
It was now comfortable for the hosts with Fulham looking a beaten outfit well before the final whistle.
Anthony Wordsworth should have added a third 11 minutes from time when he headed over from 10 yards following excellent work from McGoldrick and Luke Chambers.
McGoldrick called Joronen into action from the corner of the penalty area after yet more tenacious play by Jay Tabb before Fulham pulled a goal back out of nothing.
Hoogland cut inside Tyrone Mings and his weak shot took a wicked deflection off the body of Tommy Smith to take it past Gerken's near post.
The lifeline galvanised Fulham and another deflection almost gave Patrick Roberts an equaliser, but Town held on to claim all three points.