The Championship’s leading scorer took just five minutes to become the first Blue to score 20 League goals in 15 years when he headed in from a corner.
Fulham struggled to cope with former Sunderland player all game, particularly in the first-half and just before the break, he showed a magic touch to send the ball into the corner of the net with hardly any back-lift in his strike.
Ross McCormack gave Fulham a lifeline when capitalised on a mistake in the Town box to find the net 17 minutes from time but Blues held on to give the 4000 travelling Blue Army plenty to cheer on the final whistle.
Mick McCarthy made three changes to the side that beat Sheffield Wednesday in midweek, Kevin Bru, Jay Tabb and Tyrone Mings returning to the side in place of the injured Darren Ambrose, with Jonathan Parr and Stephen Hunt dropping to the bench.
The danger signs were there for Fulham inside the first minute when Murphy set up Freddie Sears, who sidefooted at Marcus Bettinelli from inside the box.
Murphy then fired wide, Sears retrieved the ball and fed it back into the box, Shaun Hutchinson relieved to see his clearance go over the bar.
There was no respite for the Cottagers though, from the corner swung in by Tabb, Murphy was left alone to head in.
Hugo Rodallega couldn’t get his shot in after an interchange of play involving McCormack and Ryan Tunnicliffe on the edge of the Town box as Fulham looked to respond.
Alexander Kacaniklic escaped inside Luke Chambers from Parker’s cross but his pass was cleared by Tommy Smith, while at the other end Sears had a shot blocked after Teddy Bishop had set him up.
Rodallega threatened again down the right, his cross flicked on by Kacaniklic but to a blue shirt, then Sears’ backheel in the Fulham box fell to a relieved Bettinelli.
Rodallega almost got in on Lasse Vigen Christensen’s pass 15 yards from the Town goal, Bart Bialkowski then out quickly to prevent the Fulham frontman getting in again.
Bialkowski forced Kacaniklic’s shot behind for a corner, Parker sending a curler just over as the Cottagers forced the play.
Sears had a gilt-edged chance to extend Town’s lead on 35 minutes though, the ball falling into his path after a deflection off Nikolay Bodurov but Bettinelli forced the shot away with his feet.
The Fulham ‘keeper did just as well seconds later to deny Bishop, then Murphy, who the home side just couldn’t handle down Blues’ left, had another effort cannon to safety.
It was Murphy again who struck gold just before the break, the Irishman showing all the confidence in the world to swerve the ball into the bottom corner from the edge of the box.
Parr replaced the injured Tabb before the interval as Town walked off to great applause from the travelling support and in control of the game.
Tunnicliffe sent a right foot effort just over as the second-half got underway, Parr almost getting in at the other end after Bru’s pass had been deflected goalwards.
Rodallega headed over, then Kacaniklic brought a foul out of Christophe Berra that earned the Scotland international a yellow card. McCormack sending the free-kick over the bar.
Cauley Woodrow replaced Christensen just past the hour in Fulham’s first change, Berra forcing Bishop’s corner goalwards, Bettinelli coming to the home side’s rescue as Murphy looked to get in.
Noel Hunt took over from Sears for the last 20 minutes, Fulham introducing Bryan Ruiz for Rodallega at the same time.
Kit Symons’ team were back in the game soon after, Smith failed to deal with a cross and McCormack reacted quickest to poke the ball past Bialkowski and into the net.
Tunnicliffe set up Kacaniklic on the edge of the box but he couldn’t keep his shot down as Fulham pressed for an equaliser, Town making a final change with Paul Anderson on for Bishop.
Bru picked up a booking for a foul, Cole Skuse following soon after but in between, it needed a brilliant double save from Bettinelli to deny first Mings, then Berra.
McCormack had a shot blocked as Fulham searched for an equaliser but Town saw out the game to give the biggest travelling Blue Army for a League game in 10 years the result they wanted.
The only downside for Blues was a knee injury for Hunt that required lengthy treatment before he was carried off seconds before the final whistle.