The Addicks took the lead in the 27th minute through Scott Wagstaff, who made the most of a rebound after a shot from Frank Nouble had been blocked.
Bournemouth equalised in the 30th minute when Marc Pugh headed in from close range after a misplaced back pass by Thierry Racon.
The Cherries had numerous chances to end a run of three successive defeats but went ahead in the 58th minute with a deflected shot by Danny Hollands.
But just when it looked as though Bournemouth would go on and win, the prolific Wright-Phillips shot home from the edge of the area.
Bournemouth almost snatched a winner in five minutes added on for stoppages. Pugh hit the underside of the bar and Danny Ings had a shot blocked on the line by Jose Semedo at the death.