The result caps an amazing escape for Leicester, who have been bottom of the standings for much of the campaign but survive with a game to spare after a embarking on a superb run of form.
But despite Hull’s defeat at Tottenham, Sunderland could yet be in for a nervy final week, as they need at least a point from tough trips to Arsenal and Chelsea if they are to be certain of survival.
Dick Advocaat’s side just about had the better of this encounter but could not get the breakthrough and they will need another point from somewhere if Hull manage to beat Manchester United next week.
The Black Cats started the afternoon brightly and had an early penalty shout when the lively Danny Graham crossed and Connor Wickham went down under pressure from Robert Huth, referee Martin Atkinson was unmoved.
With the Leicester defence expecting a cross, Seb Larsson then sent a clever free-kick towards the bottom corner and Kasper Schmeichel dived to his right to pull off an excellent one-handed save.
Leicester then threatened, Leonardo Ulloa inches away from getting on the end of Marc Albrighton’s nod back into the goal mouth, before Jamie Vardy had a shot blocked when the ball came back in.
That was about as good as it got for the Foxes in the first half though and Schmeichel was soon back in action, blocking a Graham volley after the forward had been picked out by a delightful floated pass from Lee Cattermole.
Wickham then got plenty of power on a half-volley from the edge of the box but it flew wide of the target and it was goalless at half-time.
Ulloa nodded a corner wide at the start of the second half but the game then went through a scrappy phase, although both sets of fans were buoyed by the news that Tottenham were beating Hull and that QPR had fought back to lead against Newcastle.
Sunderland perked up over the final 25 minutes and Patrick van Aanholt was not far away with a low drive from the edge of the box.
Adam Johnson came off the bench and made an impact, eluding Esteban Cambiasso and drawing a decent save from Schmeichel with a low shot from 20 yards out.
Johnson then sent over a fine cross from the right and his fellow sub Steven Fletcher glanced a header not far wide of the target.
However, out of nowhere, Leicester were handed a fantastic chance to score an injury-time winner when John O’Shea and goalkeeper Costel Pantilimon made a terrible mess of dealing with a fairly innocuous through pass and presented the ball to Andrej Kramaric on the edge of the box.
There were just a couple of defenders between the Leicester sub and the goal but he produced a tame effort which drifted wide of the target.
The miss proved irrelevant as far as Leicester were concerned, the final whistle coming soon afterwards and prompting jubilant celebrations from the away side.
Sunderland, meanwhile, will get their first chance to guarantee Premier League survival when they travel to the Emirates on Wednesday night.
Charlie Nicholas’s Soccer Saturday verdict
“I thought a point was a fair reflection.
“I thought Sunderland started well, with good intent. They had a good chance from a wonderful Cattermole pass and Graham caught it well, but Schmeichel was equal to it.
“Leicester were a threat but never really looked like making too many chances. So, 0-0, but it didn’t feel like a 0-0. There were a lot of young kids running about, with wholehearted determination, but it just lacked some quality.”
Sunderland: Pantilimon (6), B Jones (6), Coates (6), O’Shea (5), Van Aanholt (7), Bridcutt (6), Cattermole (6), Larsson (7), Defoe (6), Graham (8), Wickham (6)
Subs: Reveillere (6), Johnson (7), Fletcher (6)
Leicester: Schmeichel (8), Huth (6), Morgan (7), Wasilewski (6), Albrighton (6), Schlupp (6), King (5), Mahrez (5), Cambiasso (6), Ulloa (6), Vardy (6)
Subs: Drinkwater (6), Kramaric (5)
Man of the match: Kasper Schmeichel