Charlton heaped more pressure on West Brom head coach Eric Ramsay after hitting back to draw 1-1 at The Hawthorns.
George Campbell ended Albion's 405-minute wait for a goal by heading his side in front in the third minute of time added on before half-time.
But Lyndon Dykes rescued a point for the Addicks in the 70th minute to leave Ramsay without a win in his eight league games in charge.
Albion wasted numerous opportunities to add to their tally before and after conceding.
They created the first chance in the 26th minute when Campbell climbed highest at the far post to meet Mikey Johnston's cross but his header was smothered by goalkeeper Thomas Kaminski.
Charlton threatened almost immediately when Sonny Carey's firm 25-yard drive was held by Max O'Leary.
Charlie Taylor then flashed a first-time, rising effort over the bar from a loose ball from an Albion half chance.
Charlton were forced into an early change when Lloyd Jones limped off after treatment in the 35th minute to be replaced by Collins Sichenje.
Another half chance came Albion's way in the 44th minute when Alex Mowatt let fly from 30 yards but his sliced effort sailed well wide.
Albion ended their long goal drought when Campbell met Mowatt's inswinging corner perfectly at the far post to send a downward header beyond Kaminski and into the roof of the net.
Charlton made a half-time substitution with Tyreece Campbell replacing Miles Leaburn up front.
Josh Maja had the chance to make it 2-0 in the 51st minute when Mowatt's pass left him briefly in the clear, but he stabbed wide under pressure from the sliding Sichenje.
Albion had two headed opportunities from set-pieces to add to their lead but Taylor and Jayson Molumby missed from Mowatt deliveries.
Isaac Price squandered the best chance to double the scoreline when he skied over from a good position on the angle following excellent work from Molumby.
Charlton punished Albion by equalising within a minute.
Dykes latched onto Kayne Ramsay's through pass - missed by team-mate Jayden Fevrier - and kept his cool to slot through O'Leary's legs from six yards.
Johnston looked to restore Albion's lead but his shot appeared to deflect wide off Conor Coventry, before Mowatt was inches away with a shot from distance.
Substitute Jamaldeen Jimoh-Aloba's volley flew just wide as Albion chased a winner.
The managers
West Brom's Eric Ramsay:
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Charlton's Nathan Jones:
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