In the other semi, Feyenoord edged Marseille 3-2 in a pulsating clash in Rotterdam, letting a two-goal lead slip before rallying to win and take a slender advantage into next Thursday's second leg on the French south coast.
With UEFA having scrapped the away goals rule from this season, both ties remain finely poised as the teams fight for a place in the final of the inaugural Conference League that will be played in the Albanian capital Tirana on May 25.
Roma took the lead after 15 minutes at Leicester through Lorenzo Pellegrini after an incisive through ball from Nicola Zalewski set up the chance for the visiting captain who slipped his shot through goalkeeper Kasper Schmeichel's legs.
The home side dominated after that but had to wait until midway through the second half for an equaliser as Harvey Barnes burst into the box and his cross from the byline was turned into his own net by Mancini under pressure from Ademola Lookman.
Feyenoord scored twice in as many minutes early in the first half to take the upper hand in their tie at De Kuip. Cyriel Dessers and Luis Sinisterra provided the reward for a positive start in which the hosts mounted wave after wave of attacks.
But Marseille pulled a goal back with a thunderous strike from 25 metres from Bamba Dieng that flew past Ofir Marciano at his near post in the 28th minute and they were level before the break as the keeper could only parry Matteo Guendouzi's cross and Gerson fired into the net from 10 metres in the 40th.
Dessers put Feyenoord back in front straight after the break as Duje Caleta-Car left his back pass to keeper Steve Mandanda short and the Nigeria international stole in to score and give the Dutch side the advantage ahead of their trip to France.