Sunderland, who would have climbed one place to second had they won, had deserved their interval lead through Kevin Phillips' 25th goal of the season, having created the better chances in the first half.
But they were handicapped from the moment Alex Rae was sent off for his second bookable offence in the 42nd minute and conceded an equaliser via Mark Bright 13 minutes later.
"For a game of this kind there seemed to be a lot of bookings," the Sunderland manager, Peter Reid, said. "Considering we played so long with 10 men, I'm pleased we came away with a point. The lads did really well in difficult circumstances. It shows they have character."
The Charlton manager, Alan Curbishley, backed Wilkes' decision to show Rae a second card. "I thought he was a bit naive going in on the keeper like he did having earlier been booked," Curbishley said. "In any case he was lucky not to go earlier."
Sunderland had taken the initiative from the start, and Mark Bowen almost helped them into the lead after six minutes by heading across his own goalmouth straight to Niall Quinn, but the Irishman's swerving shot was well wide.
The North-east club deservedly broke the deadlock in the 37th minute when Phillips neatly headed home a cross from Darren Holloway. Their celebrations, however, were tempered five minutes later when Rae was sent off for a tackle on Sasha Ilic. He had earlier been booked for a foul on Robinson, but had escaped a yellow card when he fouled Jones.
Charlton equalised when a Jones shot was deflected and Lionel Perez did remarkably well to push the ball out, but it fell to Bright, who slammed the ball home from six yards.
Goals: Phillips (37) 0-1; Bright (55) 1-1.
Charlton Athletic: Ilic; Barness (Mortimer, 58), Bowen, Jones, Rufus, Chapple, Newton, Kinsella, Robinson (Lisbie, 85), Mendonca, Bright. Substitutes not used: Balmer.
Sunderland: Perez; Holloway, Gray, Clark, Craddock (Makin, 69), Williams, Ball, Rae, Quinn (Dichio, 77), Phillips, Johnston. Substitutes not used: Summerbee.
Referee: C R Wilkes (Gloucester).
Sending-off: Rae. Bookings: Charlton: Barness, Jones, Chapple. Sunderland: Gray, Craddock.
Man of the match: Phillips.
Attendance: 15,355.Reuse content