Everton broke the deadlock after 51 minutes of a dour game when Charlton's Icelandic defender Hermann Hreidarsson deflected the ball into his own net.
Ireland midfielder Andy Reid levelled for the home side in the 67th minute with a crisp first-time shot from the edge of the area after team mate Marcus Bent won possession.
Charlton join Watford on nine points but stay bottom on goal difference. Everton remain in the race for a UEFA Cup slot in provisional sixth place before the rest of the weekend's action.
