The second clean sheet in three games owed much to a couple of excellent saves from David Marshall.
The Canaries kicked off attacking the Barclay End goal, but were under pressure from Cardiff in the early stages and it was eight minutes before they threatened the visitors' goal.
After a slick passing sequence Alan Gow brought a save from the Cardiff keeper with a low shot from the edge of the penalty area.
On 16 minutes another fluent move ended with Sammy Clingan's fierce shot clearing the bar by a matter of inches. Alan Gow's shot was also inches away after 24 minutes.
This was quickly followed by a low, angled drive from Mooney which went wide.
The Canaries continued to take the game to the Bluebirds, but failed to turn possession into a goal.
Such was the dominance of the home side that it was two minutes before half-time before Cardiff had a clear-cut goal attempt, when Gavin Rae's low shot went a foot wide.
Marshall then blocked a point-blank shot from Rae and Eddie Johnson deflected the rebound over the bar.
The second half began with confident penalty appeals from Canaries fans and players alike when Wes Hoolahan appeared to be bundled off the ball.
However, four minutes into the half Mooney opened the scoring when he beat the Cardiff keeper to Hoolahan's through ball and in spite of taking a kick on his shin, ran on to plant a right-foot shot into the roof of the net from 11 yards.
Marshall pulled off an acrobatic save to keep out a header from Eddie Johnson from Peter Whittingham's well-flighted free-kick.
Norwich sealed victory in the first minute of added time when Gow released substitute McDonald, who raced clear of the Cardiff defence and rounded the keeper before scoring with a low, right-foot shot.
There was still time for Marshall to pull off an incredible save to keep out Roger Johnson's downward header from Ross McCormack's free-kick.