The West Yorkshire outfit were outplayed for large sections of the game, but The Whites took their chances and secured all three points.
Danny Mills made his Boro debut and had the chance to score against his former club after 10 minutes, but he failed to get his header on target.
Leeds broke the deadlock after 16 minutes when Lamine Sakho registered his first goal for the club when he got on the end of Jermaine Pennant's pass before slipping the ball under Mark Schwarzer.
Boro pushed forward and levelled the game on the hour mark when the influential Gaizka Mendieta sent Szilard Nemeth clear and the Slovak finished past Paul Robinson.
The home side then took the lead just minutes later when again Mendieta created the chance, this time for Juninho who curled home a great effort from the edge of the area.
Leeds, though, showed real resolve and grabbed an equaliser on 72 minutes when Zoumana Camara found himself unmarked in the area and he met Pennant's corner in great style to find the back of the net.
Boro pushed forward and had a number of chances to kill Leeds off, but they could not find the back of the net and were punished in the final minute.
Andy Davies, who had an outstanding game for Boro, slipped at the vital moment and that allowed Mark Viduka to break and he brilliantly lobbed Schwarzer to give Leeds all three points.
