Victory over Bournemouth left Gary McAllister's men just one place and one point outside the top six as they took their unbeaten run to five matches, though by no stretch of the imagination could this be called an easy win.
If Bournemouth had shown more care in front of goal they would have won and, surprisingly, the biggest offender was 17-year-old leading scorer Sam Vokes.
Premier League scouts have been watching ten-goal Vokes, who caused United plenty of problems but couldn't produce the finishing that earned him both goals in his side's recent victory over Hartlepool.
Despite being gifted an 11th-minute goal for Bradley Johnson when on-loan goalkeeper David Forde misjudged the flight of David Prutton's lob in the high wind, United huffed and puffed their way through the match against a side battling against relegation.
It wasn't until Neil Kilkenny scored the second goal with a fierce shot into the bottom corner on 63 minutes that United had a cushion and, if Bournemouth had taken their chances, they may well have won.
McAllister was delighted the goals came from midfield men Johnson and Kilkenny and the Leeds manager couldn't help drawing comparisons between Johnson and Leeds legend Gary Speed.
McAllister said: "I've been watching Bradley and there are a lot of times during games, especially when he climbs above people, when he reminds me of Gary Speed.
"He is a central midfielder playing out wide but I feel he can score goals from out there. He is our most accomplished left-sided player. The beauty of it is that he is getting into the game and having a big influence."
The glowing tribute wasn't lost on Johnson, who said: "To be compared with Gary Speed, who has played so many games in the Premiership, is flattering and I'll take it.
"My goal was a bonus. I saw their keeper and a defender go for the ball and gambled on it dropping to me. We have put that bad run of a few weeks ago behind us and now our aim is to kick on and win every game."
Striker Tresor Kandol limped off just before the end after taking a knock on the knee and will need a fitness check before Tuesday night's game.