The Spaniards, who had come from behind to knock out Manchester United in the last round, took the lead in the 26th minute through Youssef En-Nesyri.
Juve boss Massimiliano Allegri used all five substitutes in a bid to find a way back into the match during the second half.
Just when it looked like Sevilla had held out to take a defendable lead back to the Ramon Sanchez Pizjuan next week, Gatti, sent on for the last half hour, nodded in following a corner to keep the tie in the balance.
In the other semi Roma edged past Bayer Leverkusen 1-0 at the Stadio Olimpico.
Giallorossi defender Roger Ibanez saw his header saved by Leverkusen keeper Lukas Hradecky midway through the first half before the Serie A side eventually made the breakthrough just after the hour. Edoardo Bove slotted in after Tammy Abraham's initial shot had been saved.
In the semi-finals of the Europa Conference League, West Ham came from behind to beat AZ Alkmaar 2-1 in the first leg at London Stadium.
The Dutch side took the lead against the run of play at the end of the first half through a long-range strike from Tijjani Reijnders, which was confirmed following VAR review for a possible foul in the build-up.
The Irons were level in the 67th minute when Said Benrahma converted a penalty after AZ goalkeeper Mathew Ryan had punched Jarrod Bowen as he tried to clear the ball.
With 15 minutes left, Michail Antonio slotted in from close range following a corner to turn the tie around.
Zeki Amdouni struck in stoppage time as Basel won 2-1 at Fiorentina.
Arthur Cabral headed the Italians in front from a corner in the 25th minute.
Basel, though, were back on level terms with 20 minutes left through a fine individual effort from Andy Diouf before Amdouni completed the turnaround when he slotted in what could prove a crucial second goal following a free-kick.