The Addicks, who wrapped up the title against Wycombe last weekend and could still bring up a century of points on the final day, looked to be cruising to treble figures after first-half goals from Danny Haynes and Dany N'Guessan.
However Preston had other ideas after the break with Nicky Hunt pulling one back before Alexander, an 84th-minute substitute and featuring for the last time, curled home a free-kick to clinch a 2-2 draw.
Haynes fired Charlton in front in the 11th minute after North End failed to clear their lines.
N'Guessan, on loan from London rivals Millwall, struck a second in the 35th minute, capitalising on sloppy play from David Gray following a short goalkick to fire home.
But Hunt cut the deficit in half 12 minutes into the second period with a stunning volley from 25 yards and Alexander completed a dramatic comeback with a curling free-kick at close.