Charlton would have eased to a far more comfortable victory but for the fact that they were let down by some poor finishing by Danny Murphy and Shaun Bartlett.
The defeat could prove crucial for Albion as they are now in danger of being cut adrift and sentenced to an immediate return to the Championship.
They have won just one game this season and face a crucial encounter with fellow strugglers Birmingham City next weekend.
Their unhappy fans made their feelings known after the game when they booed the team off the pitch.
Albion made a bright start when Jonathan Greening and Andy Johnson both tested Dean Kiely from long range.
The former Republic of Ireland international keeper dealt comfortably with both efforts but he needed the help of Murphy to keep Charlton on level terms in the 26th minute.
A hopeful cross from Albion left-back Neil Clement slid under the foot of Charlton defender Talal El Karkouri and beat Murphy.
The ball looked set to sneak in at the far post but Murphy was perfectly positioned on the goal-line to clear the ball to safety.
It proved to be a timely intervention as Charlton broke the deadlock four minutes later with their first shot on target.
Once again, Murphy was to the fore. The former Liverpool midfielder whipped in a free-kick from the right wing that was somewhat harshly awarded when Zoltan Gera was adjudged to have fouled Dennis Rommedahl.
Murphy's centre was only half-cleared by Clement and the ball fell perfectly into the path of Republic of Ireland international Holland.
He struck a first-time shot that flew through a crowded goalmouth and past the despairing dive of goalkeeper Russell Hoult.
Albion almost equalised immediately when Gera's header dropped just wide, but it was Charlton who looked the far more potent side.
They should really have doubled their advantage on the stroke of half-time when Rommedahl fed the ball into the path of Murphy only for the former England international to drag his shot narrowly wide.
Murphy was off target again three minutes into the second half when his close-range shot flew into the side-netting after he had been picked out by a header from Hermann Hreidarsson.
Bartlett then followed the lead of Murphy with a glaring miss. He only had Hoult to beat after Jerome Thomas' cross had picked him out but somehow he fired his shot wide.
Fortunately for Charlton, Albion proved equally as unsuccessful in front of goal.
Kanu saw his 65th minute shot deflected on to the top of the net before Gera bundled a cross from Greening just the wrong side of the post six minutes later.
MAN OF THE MATCH: Danny Murphy (Charlton) - To the fore in defence and attack, the former Liverpool man produced his best performance in a Charlton shirt.