Kevin Phillips' 21st goal of the season cancelled out Greg Halford's first for Charlton and kept FA Cup semi-finalists West Brom in the hunt for automatic promotion from the Championship.
Halford, who arrived at the Valley on loan in January following unhappy spells at Reading and Sunderland, struck with a fine header on the half-hour.
However Phillips pounced 11 minutes later with a trademark finish to secure a valuable point for fourth-placed Albion.
Charlton were clinging on at times towards the end - Zoltan Gera hit the woodwork late on - but climbed back up to eighth, although with their play-off rivals all in action on Saturday they may soon find themselves further off the pace.
However, in a division where the top six have regularly suffered bouts of vertigo, it could yet prove a point gained for Alan Pardew's side.
Leroy Lita, starting his fourth game for Charlton since his loan switch from Reading, was almost gifted an opportunity to score in the opening moments when Martin Albrechtsen slipped as he chased a Nicky Weaver clearance, but he could not take advantage.
Halford came close to opening his account in the 11th minute, the right-back curling a 20-yard free-kick inches wide after Albrechtsen had fouled Lita.
Phillips' first sight of goal arrived in the 17th minute, the former England striker collecting Ishmael Miller's pass and cutting inside, only to see his shot bravely blocked by Sam Sodje.
Charlton striker Andy Gray flicked a near-post centre from Ben Thatcher wide before the lively Jerome Thomas crossed towards Darren Ambrose, who could only divert his header harmlessly over the crossbar.
But the Addicks broke the deadlock when Ambrose floated in a free-kick and Halford rose highest to guide his header back across the despairing dive of ex-Addicks keeper Dean Kiely and into the bottom corner.
Phillips planted a header wide from Paul Robinson's cross as the Baggies attempted to hit straight back.
And in the 41st minute they were level when Gera nodded Jonathan Greening's free-kick into the path of Phillips, who controlled the ball in an instant and smashed it past Weaver and in off the underside of the crossbar.
Charlton defender Sodje fluffed a gilt-edged chance to fire his side ahead again when he skewed an angled shot horribly wide.
In a tetchy second half, both sides passed up chances to win the game, although the flow of the match was spoiled by a series of niggly fouls.
Lita should have done better shortly after the break when he could only cushion Thomas' cross into the arms of Kiely, before Thomas himself sent a curler inches wide.
At the other end, Gera fired narrowly past Weaver's post and Miller had the ball in the net only to be denied by an offside flag.
Phillips fired over and Paddy McCarthy came up with vital interceptions to deny the veteran striker and Robert Koren.
And with two minutes remaining Gera struck a superb volley from the edge of the area which cannoned back off Weaver's crossbar.
Teams:
Charlton Weaver, Halford, Sodje, McCarthy, Thatcher, Ambrose (Cook 79), Holland, Semedo (Zhi 63), Thomas, Gray, Lita (Iwelumo 71).
Subs Not Used: Elliot, Fortune.
Booked: Semedo.
Goals: Halford 30.
West Brom Kiely, Hoefkens, Albrechtsen, Cesar, Robinson, Gera, Koren, Pele, Greening, Phillips, Miller (Bednar 76).
Subs Not Used: Danek, Kim, Martis, Slusarski.
Booked: Gera, Greening, Phillips.
Goals: Phillips 42.
Att: 23,412
Ref: Kevin Friend (Leicestershire).