Indeed, after Jonathan Stead and Rory Delap had cancelled goals from Leon Osman and James McFadden, they almost stole a last-gasp winner as a Delap screamer thumped against a post in stoppage time. With six games left, Sunderland will be hard pressed even to reach the 19-point mark on which they went down after their last venture into the top flight but there was at least a measure of pride on this occasion.
Ball's call to play for self-respect was answered so positively by Sunderland that a draw was the least reward they were due. "We had a right go at them," Ball said afterwards. "We deserved a point and when Rory's shot hit the woodwork at the end I must admit I looked towards the sky and said, 'any chance of some luck, mate?'"
Stead's goal had been his first for the club more than nine months after joining them for £1.8 million last summer, which says a lot about one of the shortcomings that cost Mick McCarthy his job. But they have not ended up in this predicament by keeping clean sheets and just as porous defending proved their undoing when Osman gave Everton their early breakthrough, so it did when McFadden restored their lead.
In the first instance, James Beattie's header from a Gary Naysmith cross might have been turned in by Simon Davies before a nudge from Osman diverted it across the line. In the second, facing a long throw from Phil Neville, Gary Breen failed to execute what should have been a routine clearance and allowed McFadden to pounce with a sharp finish.
"It looked as if we would run out comfortable winners and we had the chances to do so but we abused our opportunities today," said the Everton manager, David Moyes.
Worse still, his side defended no more competently than their opponents.
Stead's first goal in his 17th start certainly benefited from Everton's failings in that department as Chris Brown flicked on Grant Leadbitter's corner to find their team-mate lurking at the far post and only too willing to accept a simple tap-in.
Everton appeared to be guilty of complacency after going in front. As Moyes had intimated, after six straight home wins they probably believed they would find a straightforward route to another. But if they were already heading for a rocket from their manager at 2-1 in front, they guaranteed themselves one by conceding a second equaliser with nine minutes remaining, Delap nipping in front of Tony Hibbert to meet a Dean Whitehead cross and thunder a header beyond Richard Wright's reach.
Sunderland almost gave away their hard-earned gains within a minute by leaving Neville unmarked in the middle of the penalty area. Happily for them, their goalkeeper Kelvin Davis stuck out a foot to save and despite a scary closing passage in which Beattie thought he should have had a penalty, the visitors not only survived but narrowly missed out on an unexpected victory.