Former Liverpool midfielder Murphy converted a ninth-minute penalty, after the pacy Jerome Thomas was brought down, and tapped in a second from another swift raid just after the half-hour at The Hawthorns.
Although Curtis Davies capped his home debut with a headed goal early in the second half, Alan Curbishley's side held on for a fourth win on the road this season.
West Brom could have been forgiven for being distracted by Premiership top scorer Darren Bent but it was the speed of the visitors' wide men which caused them discomfort. They were caught out twice with dire consequences but it could have been worse for the midlands club as Charlton shaped the result in the initial 45 minutes.
A pass from Murphy found the former Arsenal player on the left touchline and as he cut into the box he left Steve Watson in his wake and was brought down as a result.
It was as easy a decision as referee Chris Foy will have to make all season and Murphy stepped up to send Chris Kirkland the wrong way with his ninth-minute penalty.
Murphy and Alexei Smertin, who missed Charlton's defeat to Chelsea last week as per the terms of his loan agreement, bossed the midfield throughout the opening half, causing the hosts to revert to hopeful long balls much to the displeasure of the crowd.
The nearest Bryan Robson's side came to testing goalkeeper Stephan Andersen was just a minute after the Londoners went ahead as Zoltan Gera fizzed a shot narrowly over the top from distance.
It was a different story for Kirkland, however, as twice in swift succession he kept his side just one goal adrift.
First, he got down well to turn away a Murphy header from a pinpoint cross by Dennis Rommedahl. Then when Rommedahl found space again in Charlton's next attack, a move involving Smertin and Luke Young, he picked out Thomas on the edge of the area only for Kirkland to fingertip the ball over the bar at full stretch.
But Kirkland, on a season-long loan from Liverpool, could do nothing seconds after the half-hour mark as Charlton doubled their advantage.
When a Young challenge deep in his own half cannoned off Jonathan Greening there appeared little danger with Rommedahl seizing on the loose ball.
However, the Dane justified his reputation as one of the speed merchants of the top flight by outstripping Greening to advance deep into the West Brom area and square for Murphy to sidefoot in from six yards.
The two-goal difference was well justified at that stage of the encounter and had Campbell's header a minute before the break - West Brom's first effort on target - carried more venom it would have been an injustice.
West Brom manager Robson reacted to the poor first-half showing with the immediate introduction of Diomansy Kamara, reverting to a 4-5-1 formation to counter Charlton's shape in the process.
It was a move which reaped a dividend within six minutes as the home side, whose extra vigour was evident from the first whistle, got back into things through new £3million signing Curtis Davies.
When a corner from Earnshaw was only half cleared, Ronnie Wallwork headed the ball goalwards and former Luton defender Davies glanced it into the net. Within seconds West Brom went close to an equaliser as Gera was left unattended on the right of the area only for the Hungarian to fail to pick out a team-mate with a ball which scurried across the six-yard box.
Gera swivelled to volley goalwards 11 minutes from time but struck his effort straight at Andersen and the goalkeeper also scooped an injury-time header from Kamara over the bar to make sure of the points.
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