Mancini got the final touch midway through the second half as he tried to stop Ademola Lookman turning in a low ball driven into the six-yard box by Harvey Barnes.
That brought Leicester level in their first ever European semi-final after Lorenzo Pellegrini had given Roma an early lead at the King Power Stadium.
The tie, which pits Mourinho against Brendan Rodgers, his one-time protege on the coaching staff at Chelsea, is now poised ahead of next week’s return in Italy.
Mourinho is hoping to add the new third-tier European trophy to his collection having won two Champions Leagues, a UEFA Cup and a Europa League during his managerial career, and Roma could not have asked for a better start.
They went ahead on the quarter-hour mark when Nicola Zalewski collected the ball on the left and powered forward before playing in captain Pellegrini to fire low past Kasper Schmeichel in the Leicester goal.
Last season’s FA Cup winners, who dropped into the Conference League after going out of the Europa League in the group stage, were then dealt a blow as Timothy Castagne was forced off midway through the first half.
Lookman tested goalkeeper Rui Patricio from range just after the half-hour mark but it was the second-half introduction of Barnes that proved crucial in getting the Premier League side back on level terms.
Barnes replaced Marc Albrighton at the same time Kelechi Iheanacho was sent on for Jamie Vardy, the veteran forward making his first start since early March following his latest injury setback.
It was Barnes who drove into the box before drilling a low ball in from the left side of the area towards Nigerian international Lookman. Italian international defender Mancini ended up helping the ball over the line to make it 1-1.
Rui Patricio then tipped an Iheanacho shot around the post and Leicester — whose former striker Gary Lineker was watching from the stands — will have to find a way of winning in Rome if they are to reach the final in the Albanian capital Tirana at the end of next month.
– Dessers double fires Feyenoord –
Feyenoord beat Marseille 3-2 in Rotterdam, throwing away a two-goal lead before being gifted what proved to be the winner on the night right at the start of the second half.
Colombian forward Luis Sinisterra laid the ball off for Cyriel Dessers to open the scoring for the Dutch side in the 18th minute, and Sinisterra doubled their lead just two minutes later, sweeping home from a Reiss Nelson assist with his shot deflecting in off Valentin Rongier.
In a remarkable game between two former European Cup winners, Marseille pulled a goal back in the 28th minute when Cedric Bakambu played a ball into the path of Bamba Dieng and the Senegal striker smashed in a shot from just outside the area.
The French visitors were level five minutes before half-time when Matteo Guendouzi’s low cross into the box from the right was turned out by Feyenoord goalkeeper Ofir Marciano and Brazil midfielder Gerson arrived to smash in the loose ball.
Yet, in a raucous atmosphere at De Kuip, Feyenoord went back in front just 11 seconds into the second half as Duje Caleta-Car’s short backpass was intercepted by Dessers and the Belgian-born Nigerian international snapped up the chance.
Marseille must now overturn the deficit when the teams meet again at the Velodrome next Thursday.