The Black Cats, who dumped Chelsea out of the Capital One Cup in midweek to book a place in the semi-finals, could not repeat the dose when they needed it most to leave themselves firmly rooted to the foot of the Barclays Premier League table.
Sunderland have now won just four of their last 32 league games, and a paltry tally of 10 points from their opening 16 fixtures of the season leaves them in pole position to slip out of the top flight unless they can engineer a major fightback.
Defender Wes Brown, sent off in stoppage time for a foul on substitute Ricky van Wolfswinkel, came closest to a winner when he hit the outside of the post with a 57th-minute header, while Ki Sung-yueng missed the target with Canaries keeper John Ruddy missing in action.
But despite the Black Cats stretching Norwich repeatedly after the break, they were unable to find the breakthrough to leave the bulk of a crowd of 37,778 fearing the worst.
Norwich had the better chances in a first half which saw neither goalkeeper unduly stretched.
Canaries stopper Ruddy was not called upon until the 37th minute, when he had to get down well to claim a shot from distance from Phil Bardsley - the full-back remains the club's joint-top scorer, a reflection of their difficulties.
Vito Mannone was busier at the other end, turning away Nathan Redmond's 13th-minute strike and then beating away a Gary Hooper piledriver five minutes before the break.
Hooper had earlier been left kicking himself after John O'Shea had completely misjudged Martin Olsson's left-wing cross, which hit the astonished striker in the chest before he could react.
For their part, most of Sunderland's efforts came from distance with Ki, Sebastian Larsson and Lee Cattermole all wayward before Bardsley tested Ruddy.
However, the keeper was relieved to see Jozy Altidore's deflected shot drop just wide of the far post after Brown had headed down Bardsley's 36th-minute free-kick.
The home side returned knowing they had to be much, much better, and they started encouragingly with Fabio Borini winning an early free-kick which Larsson saw deflected over the bar.
From the resulting corner, Bardsley and team-mate O'Shea collided, leaving the Republic of Ireland international nursing a shoulder injury which needed treatment on and then off the field.
But his side had a glorious opportunity to take the lead when Cattermole picked out the unmarked Brown beyond the far post and he controlled before stabbing the ball inside to Ondrej Celustka.
The full-back looked odds-on to score, but he delayed and Johan Elmander managed to bundle the ball behind with the home fans appealing in vain for a penalty for his challenge.
But as the Black Cats committed men to the search for the opening goal, they put the Canaries under pressure and they almost cracked with 64 minutes gone when full-back Steven Whittaker thumped and attempted clearance against team-mate Michael Turner and the ball dropped into the path of Borini.
However, as he waited for it to settle, the cover arrived and he eventually prodded his shot tamely at the keeper.
But Hooper should really have put Norwich ahead four minutes later when Robert Snodgrass picked him out at the far post unopposed, only to see him head wide.
Sunderland boss Gus Poyet decided the time was right to replace Altidore with Steven Fletcher, and the newcomer might have made his mark almost immediately when Bardsley flicked Larsson's 70th-minute corner towards him.
The Scotland international could not make meaningful contact, but when Turner's sliced clearance dropped to Brown at the far post, he headed against the outside of the upright.
Norwich should have taken an 82nd-minute lead when van Wolfswinkel was played in on goal, but could not beat Mannone.
But Poyet was left with his head in his hands seconds later when Ruddy rushed from his box but was beaten to the ball by Borini, who squared for Ki.
Turner got back on to the line with his keeper hopelessly stranded, but the South Korea international lifted his shot from 20 yards over the bar, and the home side's fortunes took a further turn for the worst at the death when Brown saw red for hacking his way through van Wolfswinkel from behind.