The home side - who lie bottom of the Premier League table - were looking to arrest a run of five games without a top-flight victory but failed to find a way past a stubborn Norwich defence.
In a first half devoid of quality, Fabio Borini came closest for the hosts, drilling an effort wide from the edge of the penalty area, while Norwich's best opportunity came from Gary Hooper's driven strike.
The second half followed a similar pattern with Ki Sung-Yueng coming closest for Sunderland, while Hooper again had Norwich's best opportunity.
As the game petered out, Wes Brown was given his marching orders for a challenge on Robert Snodgrass. The draw leaves Sunderland four points adrift of safety, while Norwich remain 14th.
After scoring in Sunderland's 2-1 League Cup quarter-final upset of Chelsea on Tuesday, Borini and Ki won starts, while Snodgrass returned from a knee injury to start for Norwich.
Norwich engineered the first opportunity when Nathan Redmond cut in from the left and forced Sunderland goalkeeper Vito Mannone into a smart save at his near post and although the hosts were showing plenty of intent, they were forced into long-distance efforts.
Sebastian Larsson came closest with a strike that cleared the crossbar from 25 yards in the 20th minute and Borini then flashed an effort wide from the edge of the penalty box just after the half-hour mark.
At the other end, Hooper's strong 20-yard effort was parried to safety by Mannone.
Norwich had another chance to take the lead against the run of play, but Leroy Fer shot tamely at Mannone as both sides entered the break goalless.
The second period continued in a similar fashion with both teams failing to create clear-cut chances.
Borini almost capitalised on miscommunication in the Norwich defence in the 65th minute but stabbed his effort straight at goalkeeper John Ruddy.
For Norwich, Hooper connected with Snodgrass' centre, but his effort went harmlessly wide.
Sunderland introduced Steven Fletcher for the last 20 minutes and he caused panic from a corner that resulted in Brown heading wide from close range.
Sunderland appealed for a penalty when Lee Cattermole went to ground under a challenge from Snodgrass, but it was turned down, while Ki lifted an effort onto the roof of the net when Ruddy rushed off his line.
And they were forced to settle for a point when Brown was given a straight red card in injury time for an over-the-top challenge on Snodgrass.
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