The visitors actually took the lead when Mirko Antenucci scored after just four minutes.
But their lead lasted just eight minutes, Murphy grabbing the first of his two goals, and Leeds never recovered.
David McGoldrick stroked home a penalty to give Ipswich the lead before Murphy scored his 13th of the season just before half-time. Any hope of an unlikely comeback was ended in the 48th minute when Tommy Smith scored number four.
Ipswich comfortably saw the second half out as Leeds offered little in the way of either resistance or potency.
Leeds took the lead with just four minutes on the clock. Stephen Warnock was released into the area and the away skipper had the simple task of rolling the ball across the goal for Antenucci to tap in.
But in-form Ipswich were level soon afterwards, Luke Chambers’ decent cross being met by the prolific Murphy to head past Marco Silvestri.
Murphy went close to doubling his tally five minutes later when he met Jay Tabb’s corner but his goalbound shot was blocked by Jason Pearce.
Ipswich took the lead for the first time in the 26th minute when Warnock went from hero to villain after needlessly bundling over Paul Anderson following Jay Tabb’s hopeful ball forward.
McGoldrick made no mistake from 12 yards, calmly placing the penalty into the left-hand corner as Silvestri went the other way.
A minute later it was almost three when Murphy fired wide from close range following Stephen Hunt’s knockdown.
Ipswich were in the ascendancy and, six minutes before the break, the dangerous McGoldrick almost added a third after taking control of Tabb’s decent through-ball but shooting just wide of the far post.
And on the stroke of half-time, the home side did get their third of the afternoon courtesy of top scorer Murphy.
The striker latched onto a through-ball from Anderson to break into the box and side-foot low beyond Antenucci.
Ipswich started the second half on the front foot, winning a succession of corners and grabbing a fourth goal when Tommy Smith met Hunt’s delivery. Berra may have applied the finishing touch at the far post but the New Zealand international claimed the goal.
Murphy then came close to securing his hat-trick with a neat flick volley that Silvestri pushed away at his near post.
Chances were few and far between in the final half-hour, although Liam Cooper almost diverted into his own net late on after a mazy run by sub Teddy Bishop before Chambers headed wide from Kevin Bru’s corner.