كتب : Amro Hassan
The win lifts Luciano Spalletti's men to sixth in the table with 52 points, as Lecce remain nineteenth with 24.
The Giallorossi opened the score line on 3 minutes through skipper Francesco Totti before Matteo Brighi added the home side's second ten minutes later.
The visitors stunned Roma with a brilliant second-half comeback, as they equalized through goals from Gianni Munari and Dimitrios Papadopoulos.
However, a 59th minute penalty-kick from Totti saved the day for Roma, after the spot-kick was awarded for a foul on Brazilian striker Julio Baptista.
In another game, Fiorentina succumbed to a 3-1 defeat at the hands of Udinese at the Stadio Friulli.
A strike from Kwadwo Asamoah and a second-half brace from Gaetano D'Agostino secured Udinese the three points, whereas Dario Dainelli scored the visitors' goal.
Fiorentina are now fifth, three points ahead of Roma, while Udinese's win brings them to tenth spot in the Serie A table.