Boro picked up their first points of 2013 thanks to Curtis Main's 81st-minute header which, along with Brighton's draw with Blackburn, hands his men a four-point buffer over the play-off chasing pack.
"It's nice to get a win, it's been a while for us in the league and we need to keep the points ticking along," he said.
"It's nearly 20 years since we won at home against Leeds. It's a good achievement for this team and we deserved to win. We competed against a team that you have to compete with and on the balance of play it was right we came out on top.
"Other games can be more of a football game but Leeds put you under pressure, don't allow you to keep the ball and it becomes more of a physical battle. But we came out on top of that."
Main's goal was a moment of rare class in the game, a header back across Paddy Kenny's goal after a brilliant cross from Ishmail Miller.
Before that, two bits of brilliant defending from Jonathan Woodgate were the highlight, with the former England international twice denying Ross McCormack, once on the line and once racing back towards his own goal.
Main's moment was ruined, though, when he was sent off for a handball/dissent combination and Mowbray added: "Without being over critical of the official, he got it wrong.
"Curtis is a young boy who is starting his career off. He came to us as a free transfer from Darlington and some of the things he can do are breathtaking at times."
Middlesbrough last week