The Republic of Ireland international headed in on the hour after David McGoldrick had hit the woodwork for the third time.
Tommy Smith had given Blues the lead just past the half hour, with the biggest crowd of the season, 26, 157, at Portman Road to watch Town stretch the unbeaten run to 11 games.
McGoldrick wrapped up the points for Town in the final minute with the goal he deserved, with the three points leaving Blues just behind leaders Bournemouth as we enter the second half of the campaign and 10 points clear of seventh placed Norwich.
Town stayed with the side that beat Brentford on Boxing Day, Tyrone Mings taking a place on the bench after recovering from injury.
Jordan Cousins found the sidenetting in the first minute for the visitors, Smith responding for Blues with a header that was held by ‘keeper Neil Etheridge.
Murphy then had a shot deflected behind for a corner after Teddy Bishop had threaded a ball to him on the edge of the box.
Murphy was then hauled down and McGoldrick thumped a superb free-kick against the inside of the post on 10 minutes.
Johann Berg Gudmundsson tried his luck from distance for the visitors but his effort was wide while at the other end the ball wouldn’t fall for McGoldrick on the edge of the box from Jay Tabb’s cross.
McGoldrick then fired wide as Town pressed for the opener, Christophe Berra in the right place to see out the danger from Igor Vetokele as the half hour mark went by.
Paul Anderson fizzed in a cross that almost found McGoldrick, Berra then denied by Tal Ben Haim’s clearance six yards out but Blues would not be denied and from the resultant corner Smith smashed the ball into the net from close range after Luke Chambers headed on.
Berra was in the right place again to head off the line from Gudmundsson’s long range effort after Bart Bialkowski had denied George Tucudean, with Tucudean then sending a right foot effort over the bar from inside the box as Charlton threatened an equaliser.
McGoldrick went agonisingly close to adding a second with virtually the last kick of the half, his free-kick hitting the post and bouncing back off Etheridge to go inches wide as Town went in a goal to the good.
Gudmundsson sent a left foot effort at Bialkowski as the second-half got underway, Johnnie Jackson heading over from 12 yards as Charlton started on the front foot.
It was Town who struck again though, McGoldrick hitting the woodwork for the third time on the hour and Murphy continuing his dream season with a simple header into the empty net.
McGoldrick sent a curler just over after Tabb’s clever ball had released the frontman while at the other end Bialkowski fisted away Gudmundsson’s fierce cross.
Stephen Hunt replaced Anderson for the last 20 minutes, Bishop firing over as Town looked to wrap up the points.
Vetokele headed over, Gudmundsson seeing another strike deflected wide as time started to run out for the visitors and the victory was sealed on 90 minutes when McGoldrick got the goal he deserved.
Kevin Bru and McGoldrick then went close to adding a fourth as Blues brought 2014 to an end in style.