The visitors were architects of their own downfall, with David Nugent putting Boro ahead after only 121 seconds before Giuseppe Bellusci made it 2-0 in the 32nd minute by heading George Friend's cross into his own goal.
After Leeds striker Mirco Antenucci had seen a goal ruled out for a tight offside, Sol Bamba's slip allowed Diego Fabbrini to round the goalkeeper and score Middlesbrough's third goal with nine minutes remaining.
"I don't think the score is a reflection of the game," said Middlesbrough manager Aitor Karanka. "But the main thing is that we have won and we have another three points on the table.
"I knew this was going to be a very difficult game, and it was. We are only in September, though, and we have to keep going."
Boro have won all seven games since losing 1-0 at home to Bristol City on August 22, including League Cup wins over Burton Albion and Wolverhampton Wanderers, and have a five-point cushion in second place.
Defeat left Leeds in 14th place in the English second tier, four points below the play-off places.
Leeds manager Uwe Rosler criticised the match officials for disallowing Antenucci's goal, having initially awarded it, and also felt that Boro's Cristhian Stuani should have been sent off for repeated fouling.
"The referee had a poor day," said the former Manchester City striker.
"He got two major decisions wrong. Stuani should not have been on the field and obviously the goal too.
"He (the linesman) told me he had to ask the referee, so he wasn't sure. How can you give offside when you're not sure? He has to be 100 percent sure."