The out-of-sorts Addicks suffered a nightmare first half, and went behind just before the half-hour mark after a Simon Francis error allowed Enoch Showunmi to race clear and slot home.
But Chris Powell's men regained their confidence after the break and drew level from a 20-yard free-kick taken by the returning Miguel Llera.
They created plenty of chances to turn the game on its head, including a couple more for Llera and two for his defensive partner Christian Dailly.
Sub Nathan Eccleston almost won it at the death from close range, but although the Reds were unable to collect all three points, they will be buoyed by their recovery to end their losing run.
Source: PA
Source: PA