Emi Buendia's 27th-minute strike opened the scoring before Todd Cantwell added a second in the 70th minute as the Canaries continue their impressive form, having now won 12 of their last 16 matches.
The defeat was just their second in the last six games and Cardiff missed a chance to go level with Brentford on points for sixth place in the table.
Story of the match
After containing Norwich in the opening stages of the contest, Cardiff were almost caught out in the 12th minute as Jacob Sorensen was given space down the left and he picked out Cantwell on the edge of the box, whose shot deflected off of a Bluebirds defender.
After Teemu Pukki also saw a shot deflected, Kenny McLean timed his run onto Buendia's lovely pass perfectly and his header is just inches wide of the post.
Greg Cunningham came to the Bluebirds' rescue in the 21st minute as he took the ball away from Pukki with his foot after the Finn has been set up by Cantwell.
A minute later Pukki eluded Sean Morrison and Cantwell found him inside the box. The Norwich number nine then tried to shoot in the bottom corner, but dragged his shot wide.
Cardiff had their first chance soon after as from a free-kick Harry Wilson saw his ball met by Morrison, who headed one at Canaries keeper Michael McGovern that was held onto.
On 27 minutes, Norwich were in front. Buendia picked up the ball midway in the Cardiff half, carried it to the edge of the backline and fired a low shot past Bluebirds keeper Alex Smithies.
Two minutes from halftime, McGovern kept Norwich in front as Morrison rose up higher than Buendia and met Wilson's sumptuous cross that the Canaries keeper made a wonderful save with his right hand.
Pukki was gifted a golden opportunity to double Norwich's lead two minutes into the second half as Marlon Pack's misplaced pass sent him through, but his lob over Smithies fell wide.
At the other end, Grant Hanley bravely got in the way of a pair of shots, first clearing Wilson's shot then blocking Joe Ralls' effort, but Pack soon was stripped again and Smithies tipped Buendia's shot around the post.
Cantwell soon made Cardiff pay for all the time and space the Canaries were given, smashing his shot into the top corner from the edge of the box to double their lead, giving Smithies no chance.
The hosts almost added a third as Buendia found some space, but it went just wide of the left post. At the other end, Junior Hoilett and Morrison missed chances for the Bluebirds, the last meaningful action in a game controlled by Norwich.
Men of the match: Buendia, Pukki and Cantwell
It's not often you pick more than one player for this award, but all three were outstanding. They controlled the tempo and pace of the game, created and took quality chances and made Cardiff pay for all of the time and space being presented to them.
Norwich are headed back to the Premier League. While we aren't even at the halfway point of the season, matches like this, along with their position in the table, show the gulf in class between the Canaries and the rest of the division.
Cardiff's backline were guilty of allowing Norwich too much room to work with, Pack in particular and the Bluebirds couldn't really muster many quality chances. If it wasn't for Smithies, the scoreline could have been worse.