The Italian striker struck with a downward header in the 30th minute of a match Juventus dominated, handing Leonardo his second defeat as Inter coach since taking over from Rafa Benitez.
Inter stayed fourth, eight points behind leaders Milan who defeated Parma 4-0 on Saturday, with a game in hand while Juve climbed to sixth.
"We wanted it tonight. January was a difficult month - we had some injuries and lost form, but this is a good side and we can go very far still if we keep up the same spirit and desire," he said.
"The first half was difficult, we were slow and couldn't get men forward. The second half was very different, we got more players into the box and had chances.
"If we win all our matches, we will win the league but we take each game at a time and so far we have seven positive results out of nine."
Inter pressed and striker Samuel Eto'o had an effort saved on 82 minutes after an audacious flicked pass from Wesley Sneijder.
A minute later Eto'o kicked thin air with another presentable opportunity to sum up a disappointing evening for Inter who play their game in hand at Fiorentina on Wednesday.
Antonio Di Natale kept pace with Edison Cavani at the top of the scoring charts. After the Uruguayan's double against Roma on Saturday took him to 20, the Italian striker bagged his 17th and 18th strikes of the season in Udinese's 3-0 win at Cesena which kept them fifth.
