- Ibañez (7' OG)
- Paulo Dybala (17' Pen)
Roma, who visit Salzburg in the Europa League on Thursday, moved provisionally up to third in the standings on 41 points. They are level with AC Milan in fourth and two points behind second-placed Inter Milan who have a game in hand.
Lecce remain 14th on 24 points from 22 games.
Roma defender Roger Ibanez scored an own goal to give Lecce the lead in the seventh minute, heading into his own net while attempting to clear following a corner.
Dybala levelled for Roma 10 minutes later from the spot, firing low into the net for his eighth goal of the season after Jose Mourinho's side were awarded a penalty for a handball.
The England striker tried to catch the Lecce keeper unawares once more five minutes into the second half with a close-range header but Falcone denied him again.
"Tough game, obviously you can see from our frustration that it's not the result we wanted," Mourinho told DAZN.
"The pitch was horrible and players had a lot of problems playing with their first touch, you had to lift the ball and you also risked your ankles.
"[It's] difficult to play quality football [like this]. For this reason I don't say anything negative to my players, neither individually nor collectively."
- Gianluca Aureliano