The point, earned from behind, lifted Sunderland from 17th to 15th place in the Premier League and puts them three points clear of the danger zone.
However, only goal difference will separate them from a place in the bottom three if Wigan win their game in hand - at home to Swansea - on Tuesday.
Despite Sunderland producing a fine effort to come from a goal down with 10 men - John O'Shea scoring the equaliser in the second half - the Black Cats were trimmed from 8/1 to 13/2, a price offered by Ladbrokes, Paddy Power and bet365.
With Reading and QPR already gone, only one relegation place remains to be filled and Wigan remain favourites to fill it at a best of 13/10 (Boylesports).
However, that is likely to change if they defeat Swansea.
Norwich are rated next most likely to go down - Sky Bet offer a top price of 100/30. They, like Sunderland, have 38 points, as do Newcastle. The Magpies will sink into the drop zone if Wigan win on Tuesday and they can be backed at 9/2 (general) to go down.
Southampton, currently 14th on 39 points, and Aston Villa, 13th on 40, are on offer at 33/1 and 28/1 respectively.
Stoke have 41 points and now sit 11th after their point at the Stadium of Light. They are not mathematically safe yet but Midlands-based bet365 feel they are fine and offer 500/1 about the Potters going down.
Stoke (Pld 36 Pts 41 GD -10)
May 12 - Tottenham H
May 19 - Southampton A
Fulham (Pld 36 Pts 40 GD -11)
May 12 - Liverpool H
May 19 - Swansea A
Aston Villa (Pld 36 Pts 40 GD -21)
May 11 - Chelsea H
May 19 - Wigan A
Southampton (Pld 36 Pts 39 GD -11)
May 12 - Sunderland A
May 19 - Stoke H
Sunderland (Pld 36 Pts 38 GD -12)
May 12 - Southampton H
May 19 - Tottenham A
Norwich (Pld 36 Pts 38 GD -22)
May 12 - West Brom H
May 19 - Manchester City A
Newcastle (Pld 36, Pts 38 GD -23)
May 12 - QPR A
May 19 - Arsenal H
Wigan (Pld 35 Pts 35 GD -22)
May 7 - Swansea H
May 14 - Arsenal A
May 19 - Aston Villa H