Quakers are now 21 points from safety with 21 to play for, though they hold an inferior goal difference, so their fate is likely to be confirmed on Tuesday when they travel to Rochdale who will be aiming to seal promotion.
Relegation would have been confirmed today with a defeat, but there were few clear chances in a dull match that neither side deserved to win.
But at least a draw brought and end to Quakers' losing home run which had stretched to six games before today.
In the first half Simon Davey's side were first to show some attacking intent with winger Chris Moore twice weaving through Accrington's defence.
His first attacking foray saw a shot tipped wide by keeper Ian Dunbavin but his second came to nothing before right-back Paul Arnison let fly from distance.
The defender had an attempt with the outside of his right boot but Dunbavin was equal to the 20th minute effort which preceded two for the visitors.
Jimmy Ryan had a long-range shot go high over the crossbar before striker Michael Symes chested down a right-wing cross but his careful volley towards far side of goal sailed narrowly wide of goal.
As the half progressed the two toothless sides struggled to threaten the respective goalkeepers, though Quakers forward Tadhg Purcell had an effort from shot a narrow angle pushed wide by Dunbavin.
Five minutes into the second half Robert Grant's 20-yard free-kick went over the bar and the same player was then denied by keeper Shane Redmond who parried wide a shot as the left-winger bore down on goal.
It was the visitors who made the brighter start to the second period and Ryan lifted the ball over the bar after a nicely worked corner routine that involved dummies from two team-mates.
A Darlington counter-attack initiated by Mor Diop, back in the side after a hamstring strain, led to a glorious opportunity but Purcell's wasted the chance.
Diop passed to Purcell who in turn should have handed Moore a shot at goal, but the Irish striker opted to shoot from 25 yards and his effort was charged down by midfielder Luke Joyce.
Purcell almost atoned soon after, plucking the ball out of the sky with a delicate touch, but his resulting shot was stopped by the onrushing keeper's legs.
In the final five minutes Redmond made an impressive double save, keeping out efforts from Darren Kempson and then Grant, before Ryan evaded Darlington left-back Stuart Giddings but the Accrington winger got it all wrong in the penalty area.
Giddings was handed his chance, in place of Andrew Milne, after recovering from a groin strain while Diop came in for Curtis Main who suffered an ankle injury in training on Friday.
But neither did themselves much good, and nor did many of their team-mates, in a disappointing display that Davey will struggle to take positives from.
He will at least be pleased that his team kept a rare clean sheet, only the club's fifth in 39 games, with what was Quakers' first scoreless draw.
*After the game Davey revealed that he has released midfielder Ross Chisholm and striker Patrick Deane.
Booking: Giddings (86, foul)
Referee: Andy Woolmer (Northamptonshire)
Darlington (4-4-2): Redmond; Arnison, White (Byrne 68), Miller, Giddings; Moore (Convery 70), G Smith, Dempsey, Gray; Purcell, Diop (M Smith 64). Subs (not used): Liversedge, Milne, Groves, Mulligan
Accrington Stanley (4-4-2): Dunbavin; Lees, Kempson, Edwards, Winnard, Ryan, Procter, Joyce, Grant, Symes, Kee (Miles 45). Subs (not used): Bouzanis, McConville, Mullen, Murphy, King, Flynn