Terry Connorâ€™s struggling side gained one point back on second-bottom Blackburn Rovers, who lost 3-0 at Swansea City, but they still sit five points in arrears of their nearest rivals and eight points away from safety with the draw not enough to give them survival hope.
The visitors were unlucky not to come away with the maximum quota of points as Black Cats keeper Simon Mignolet came up with a brilliant 81st minute save to deny Steven Fletcherâ€™s goalbound header whilst the home side also had a close shave when Seb Larssonâ€™s flicked Stephane Sessegnonâ€™s through ball over the bar with two minutes left.
In the 16th minute, Sunderlandâ€™s James McClean was close to opening the scoring but side-footed into the side netting after he was found by himself at the back post by a Sessegnon pass.
Mignolet came up with his first real save just prior to the hour-mark when he scrambled across goal to hold Anthony Fordeâ€™s effort from range before Wolves gloveman Wayne Hennessey was on hand to deny McCleanâ€™s 72nd minute from Craig Gardnerâ€™s pinpoint cross.
But in the end, neither side were able to breach the opposing defence as Martin Oâ€™Neillâ€™s Sunderland, who have now failed to win in five, remained safe in ninth position as Wolvesâ€™ survival hopes look even slimmer.
Stadium of Light, Sunderland â€“ 37,476
Yellow cards: SUN - nil
WOL - Richard Stearmand 86â€™