Ryan and Elliott Bennett were the heroes for the home side as they relieved the tension that was rolling down from the stands after the home side failed to break the deadlock in the first half.
And despite Reading pulling a goal back, they held on to claim the three points that put Chris Hughton's side eight points clear of the drop zone with just four games to go.
In contrast Reading look certain to return to the Championship just 12 months after winning promotion from the second tier.
Nigel Adkins' side remain bottom of the table, 10 points from safety, and relegation would be confirmed in the unlikely event of Aston Villa winning at Manchester United on Monday.
Norwich made a strong start and Robert Snodgrass shot wide before Javier Garrido drilled in a low shot which Alex McCarthy gathered at the second attempt.
Canaries defender Michael Turner had to be replaced in defence by Ryan Bennett after 18 minutes, but Reading tested the hosts too little and too infrequently in the opening half.
Norwich started the second half as brightly as they had done the first, and McCarthy denied Kei Kamara before the pressure finally paid off.
Grant Holt's header from Snodgrass' set-piece, was saved, but the ball fell for Ryan Bennett, who took one touch and swept it in left-footed for his first Norwich goal.
The second came two minutes later as McCarthy was caught in no-man's land trying to reach a Snodgrass cross and Elliott Bennett shot through his legs and into the net.
Reading pulled a goal back with 18 minutes remaining when Garath McCleary was allowed to run at the Norwich defence and he hit a fine long-range strike past Mark Bunn.
But there was to be no miraculous comeback and Norwich held on for a vital win.