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.
Story continues below...
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.
A GUARANTEED PROFIT OF AT LEAST £36.50 ON SOUTHEND v DONCASTER
Did you know that it is possible to win money on Friday evening's League One Play-Off clash between Southend and Doncaster, whatever the result?
The game kicks off at 7.45pm and we can guarantee you a profit of at least £36.50, whatever the result of the match. All you have to do is follow the simple instructions below and then sit back and enjoy the game. At full-time, you will be at least £36.50 better off, whatever the result of the match.
We must point out that if you want to take this bet, you should do it now because if the odds change, then the figures here will be invalidated. If they have changed, let us know and we will rework the bet for you.
You can still do this if you have a Betfair account but your overall profit will be reduced by £25.00 as you won't receive the £25.00 cashback as an existing account holder.
If you are unsure about this bet, you are most welcome to call us on 01642 223229 and we will help you as much as we can.
We're going to lay out a total of £71.00 on the Southend v Doncaster match and we will collect £107.50 if Doncaster win, £107.50 if Southend win and £107.81 if it's a draw. That's a minimum profit of 51%, a much higher interest rate than you will get in any high street bank.
Here's how it's done. Just follow these simple instructions.
1. Open an account with Coral. It is really important that you enter the bonus code of CORALTD when prompted. This is to ensure that you receive your bonus.
Open an account with Betfair. It is really important that you enter the promotional code of BFB425 when prompted. This is to ensure that you receive your bonus.
Place £20.00 on Doncaster at 2.75 (7/4) with Coral.
Coral will now add a £10.00 bonus to your account. Place this on Doncaster as well. You will now have £30.00 riding on Doncaster.
Back the draw with £26.00 at 3.3 (9/4) (or higher if available) with Betfair.
Place £25.00 on Southend at 2.15 (23/20) with Extrabet.
Extrabet match your first bet up to £25 so you will now have £50.00 riding on Southend.
The £25.00 matched bet will not show in your account but you can read all about how it works on the Extrabet site. It's the purple box that says '£25 FREE BET FOR NEW CUSTOMERS' on the top right hand side. Click here to visit the Extrabet site.
If you are unsure about placing these bets, please feel free to mail us or call us on 01642 223229 and we will talk you through it, no problem at all. There is no such thing as a stupid question.
You have temporarily laid out a total of £71.00 on the Southend v Doncaster match. I stress, temporarily... Now sit back, crack a beer open and enjoy the match.
4. Here's what happens at the end of the game.
If Doncaster win, you collect £107.50. That's £82.50 from Coral plus a £25.00 cashback from Betfair.
If it's a draw, you collect £107.81. That's £82.81 from Betfair plus a £25.00 cashback from Betfair.
If Southend win you collect £107.50. That's £82.50 from Extrabet plus a £25.00 cashback from Betfair.
5. This means that the worst case scenario on the Southend v Doncaster match is no draw and you make £36.50 profit. However, if it is a draw you make £36.81. That's a minimum profit of 51%, a much better rate of interest that you would get at any high street bank or building society.
6. It is absolutely vital that you click on the links on this page to open the accounts with the two bookies and enter the correct bonus codes or you may not qualify for the bonuses.
Also, before you place your bets, you should check that the odds haven't changed. If they have, let us know by mail or phone us on 01642 223229 and we will rework the bet for you.
Please feel free to contact us or phone us on 01642 223229 if you have any questions at all about this bet and we will help you as much as we can.
Please note that the bonuses are valid for new customers only so if you already have an account with one or more of the bookies we are using, you won't be able to do this. If that is the case, mail us or phone us on 01642 223229 and we'll create an alternative bet for you using different bookies.
This method of betting was used very successfully during the 2006 World Cup and you can read all about how it was done right here.
We guarantee this bet
It's understandable that some people will not believe that it is possible to do this. "What's the catch?" I hear you asking. My answer to that question is that we have been publishing arbitrage bets for four seasons now and literally hundreds of people have profited from following the advice on these pages.
Only twice has our refund guarantee been triggered and that was when we did all the figures wrong and sent refunds out to those who had followed our advice and made a small loss.
Our refund guarantee works like this. If this bet doesn't work like we say it will and you end up out of pocket, we will refund your losses. Simple as that.
That means that you simply cannot lose on this, whatever happens and even if we messed up the numbers.
The only stipulation here is that you must click on the links on this page to be eligible for the refund guarantee, not that you'll be needing to claim anyway. Just enjoy the profit and stay posted for many more of these throughout the season.