Garry Monk needed a win to secure his position as Leeds manager
After a goalless first-half where Cardiff hit the woodwork twice, United took the lead in the 62nd minute through Chris Wood's penalty.
The lead was doubled 20 minutes later when Pablo Hernandez made a solo run into the box and fired into the top corner from 18 yards out.
This is Monk's second victory in a row having overseen a 2-1 win over Blackburn on Tuesday, and sees United climb away from the relegation zone.
The victory condemned Cardiff to a fourth successive defeat. They find themselves languishing in 22nd place
Here's a look at three players who shone for the Whites:
The Swedish centre-back joined on a season-long loan from Torino in August and is quickly becoming a fan favourite among the Elland Road faithful.
Jansson showing the amount of effort expected of him against Huddersfield Town
Jansson put in a commanding performance at the heart of Leeds' defence, snuffing out any Cardiff attacks with ease. He was an oasis of calm at every dead-ball situation, with Cardiff having 12 corners and not managing to trouble the scorers thanks to the attentions of the 25-year-old.
It wasn't just in his own box that Jansson caused Cardiff trouble. It was Jansson who was manhandled at an attacking corner that won Leeds the penalty from which they took the lead.
Jansson did as much as - if not more than - anyone else in a Leeds shirt to win this game.
The 24-year-old Kiwi broke the deadlock with his score from the penalty spot, sending Cardiff goalkeeper Amos the wrong way, capping off a superb all-round performance that earned him a round of applause from the travelling fans when he was subbed off late on.
Wood could have opened the scoring even earlier when he forced Amos into an excellent save, whilst he also shot wide from a tight angle just before he scored his penalty.
Wood celebrates his goal against Sheffield Wednesday earlier in the season
He has certainly found his scoring boots this season - having also got on the scoresheet during Tuesday's win over Blackburn - while he now has four goals in total putting him joint-second in the Championship top goalscorers at an average of one goal every 157 minutes.
With Leeds averaging just over one goal per game, they'll need Wood to continue his excellent run of form and keep firing them up the table.
The 25-year-old defender combined with Jansson to ensure that the Leeds goal was never breached in an almost faultless captain's performance.
Bartley in action for Leeds against Sheffield Wednesday
Whilst Jansson has received most of the plaudits for an outstanding, no-nonsense performance, Bartley matched the Swede for presence, managing to shepherd a Cardiff team that engineered 11 shots on goal alongside a plethora of corners.
Despite the scoreline, Bartley was part of a unit that found itself under the cosh for large parts of the game, making 36 clearances and 22 headed clearances as their opponents three themselves forward in front of their home fans - most notably when Ricky Lambert found himself through on goal only for Bartley to cover the ground and clear the danger.
Leeds have had problems with conceding too many goals earlier this season, but in Bartley and Jansson, Monk seems to have found a pairing that can make Leeds a formidable outfit.
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