Murphy's two first-half goals earned high-flying Charlton their fifth win in six games with their only slip-up coming at the hands of champions Chelsea last week.
Charlton, who have now won all the Premiership games they have played at The Hawthorns, were well worth their 2-0 half-time lead as they dominated proceedings in the opening 45 minutes.
Their advantage would have been even greater but for goalkeeper Chris Kirkland who pulled off two smart saves.
Albion were left chasing the game after just nine minutes when referee Chris Foy ruled that Albion right-back Steve Watson had fouled Jerome Thomas to bring to an end his surging run into the area.
Foy had no hesitation in pointing to the spot and Murphy calmly rolled the ball home as he sent his former Liverpool team-mate Kirkland the wrong way.
Once Charlton had broken the deadlock the only surprise was that it took them another 22 minutes to increase their advantage. That was solely down to the heroics of Kirkland who beat away a header from Murphy and pushed a rising drive from Thomas over the bar after tricky winger Dennis Rommedahl had set up both chances.
But Rommedahl made it third time lucky in the 31st minute when he cashed in on a lucky ricochet. When Paul Robinson challenged the Charlton right-back Luke Young the ball bounced off the knee of Albion midfielder Jonathan Greening and straight into the path of the flying Rommedahl.
Greening tried to keep pace with the Dane but never got near him. Rommedahl was able to reach the goal-line and send over a cross that Murphy was able to calmly turn home from six yards.
Albion were in danger of being over-run at this stage, but did eventually spark themselves into life in the final five minutes of the half when skipper Kevin Campbell twice went close only to see his shot blocked by Chris Perry and his header saved by Stephan Andersen.
It was to prove to be a vital spell of play for Albion as they were able to take the momentum they had built up during that period into the start of the second half.
With Diomansy Kamara also replacing the ineffective Andy Johnson, Albion were transformed and gained their reward after 51 minutes through Clint Davies.
Perry could only head a Robert Earnshaw corner out to Ronnie Wallwork who in turn played the ball back into the area. He picked out Davies who had the simple task of nodding past Andersen from six yards.
For the first time in the game, Charlton were rattled and Zoltan Gera was inches away from dragging Albion level three minutes later when his shot flew wide.
When Greening fired just wide in the 58th minute it seemed only a matter of time before Albion would draw level but Kamara drove over the bar after 75 minutes and then Gera was denied by Andersen.
Davies then saw his stoppage-time header saved as Charlton just about managed to hold on to the advantage Murphy had given them as they secured their fourth successive away win.
MAN OF THE MATCH: Danny Murphy (Charlton) - Two coolly taken goals and an impressive all-round display as the former Liverpool ace produced the kind of form that must catch the eye of England chief Sven-Goran Eriksson.