After failing to find the net in their two games since Claudio Ranieri took charge, the hosts took control of the game from the off and managed to rectify that on 12 minutes.
Stephan El Shaarawy produced an excellent angled through ball to find Alexis Saelemaekers in the box, and while on the slide, he managed to do just enough to get the ball past the onrushing goalkeeper and it dribbled into the net.
It looked like that would be enough to see Roma go into the interval 1-0 up, but substitute Saud Abdukhamid was penalised for a body check on Lassana Coulibaly, who was sent sprawling to the deck.
Nikola Krstovic kept his cool from the spot and smashed the ball home to send the teams in level at the break.
Perhaps sensing that a win was there for the taking, Marco Giampaolo made a triple substitution at half time.
Despite the plethora of fresh legs for Lecce, Roma came close to scoring shortly after the restart, but Paulo Dybala dragged a shot wide of the post.
Approaching the hour mark, the hosts needed someone to step up, and their captain Gianluca Mancini obliged, launching himself at an El Shaarawy cross to send a diving header into the back of the net to the delight of the home crowd.
Giampaolo responded with another two changes, but it was Ranieri’s men that made the difference five minutes later.
Abdulhamid atoned for giving away the earlier penalty by picking out Niccolò Pisilli, who tucked the ball away in the bottom corner with a precise finish.
Lecce had no answer and the hosts still had time for one more when Manu Kone added a fourth.
After winning by a scoreline that few would have expected at half-time, Roma have climbed to 11th, with any simmering relegation fears amongst their fans significantly calmed by tonight’s victory.
That is in sharp contrast to Lecce, who sit just two points above the drop zone in 16th.