The Republic of Ireland international cancelled out Mirko Antenucci’s fourth minute goal with a header soon after and could have added to the scoreline before David McGoldrick put Blues in front on 26 minutes with a penalty.
Murphy struck again right on half-time to equal his goal tally of last season at 13 and three minutes into the second-half, Town made it four, Christophe Berra getting the last touch after Tommy Smith had headed on.
Town made one change from the side that won at Charlton last week, Berra back from suspension and coming in for Jonny Parr.
It was Leeds who were out of the blocks the quicker and after four minutes the Whites were ahead, Stephen Warnock found space down the left and Antenucci was left to guide the ball into the net from close range.
Town responded, Paul Anderson’s cross was cleared by Jason Pearce as Murphy threatened but the Republic of Ireland wouldn’t be denied on 12 minutes, the striker powering a header into the net from Luke Chambers’ excellent cross.
It needed a brilliant block from Berra to beat out Alex Mowatt’s shot after Adryan had set him up, then at the other end Murphy was denied by Pearce’s intervention as a second goal looked inevitable.
Bart Bialkowski saved comfortably from Antenucci’s header, Tyrone Mings at full stretch to clear from Souleymane Doukara as the visitors carried an attacking threat on the break.
It was Blues were edged in front though midway through the first-half, Anderson was pushed in the back by Warnock and McGoldrick did the rest with ease from the spot.
Town could have added a third within a minute, Stephen Hunt headed the ball back across goal, Murphy controlled under pressure but dragged his shot wide.
McGoldrick curled a right footer over from the angle of the box, then sent another effort just wide after bursting into the box before on the stroke of half-time Blues did make it three, Murphy escaping down the right and sliding the ball past Marco Silvestri and into the net.
Blues wrapped up the points inside four minutes of the second-half, Mings had already seen a cross hacked clear but from Hunt’s corner, Smith glanced the ball towards goal and Berra nudged it over the line.
Murphy was close to a hat-trick after his volley was pushed away by Silvestri following McGoldrick’s clever chip as Blues threatened at every turn.
Mick McCarthy freshened it up with Teddy Bishop, Kevin Bru and Conor Sammon all joining the action which remained one way traffic towards the Leeds goal, Bishop weaving his way inside the Whites’ box but his cross was cleared by Pearce as McGoldrick threatened a fifth.
The win stretches Town’s unbeaten record to seven, with Blues unbeaten at Portman Road since August.