Striker Curtis Main scored the only goal of the game as Boro registered their first win in the Championship in 2013 ending a run of five successive defeats.
Mowbray told reporters: "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."
Middlesbrough are sixth in the Championship table on 50 points, six points off the automatic promotion places.