Mikel Arteta's team went top of Group B thanks to the Brazilian striker, who set up Gabriel Martinelli's opening goal with a brilliant turn and pass. He then doubled the Gunners' lead with a devastating finish.
After Lens's 1-1 draw at home against PSV Eindhoven, who are tied with Sevilla on two points, Arsenal increased their lead to six points, one more than Lens.
Following an outstanding and fierce display in a draw against La Liga leaders Real Madrid on Saturday, Diego Alonso's players put up a strong effort in the Uruguayan's second game in command.
Jesus, who has scored in each of his team's tournament matches, was the difference maker in an exciting match between Arsenal and Andalusia, despite the latter having a stronger offensive edge.
Before the game, Sevilla flaunted banners celebrating their record seven Europa League victories, but in the center of their defense is Sergio Ramos, a four-time Champions League winner.
The hosts held Arteta's team at bay for the most of the first half, which was marked by Martinelli opportunities, thanks to the 37-year-old's effective defense.
Orjan Nyland, the Sevilla goalkeeper, rapidly darted off his line to divert Martinelli's effort, save the first one and sent it out for a goal kick.
At the boisterous Ramon Sanchez Pizjuan Stadium, the hosts took control in the pouring rain. Lucas Ocampos missed several opportunities to score, and Arsenal goalkeeper David Raya appeared uneasy when under duress, giving the ball away.
Although some supporters wanted to see Aaron Ramsdale returned to goal on Saturday's Premier League tie against Chelsea, Arteta stood by the Spain international despite his two errors.
Just seconds before Arsenal grabbed the lead, Sevilla had their finest chance of the first half when Youssef En-Nesyri broke into the area and missed the target by a short margin.
Gabriel Jesus maneuvered wonderfully in midfield to confuse two Sevilla defenders and open up the pitch before releasing Martinelli through on goal with a fast cross after another Sevilla attack was cut short in stoppage time.
Ramos was unable to come up to the Brazilian as he calmly rounded Nyland and slotted home on his Champions League debut.
Jesus resolute
When Arsenal last qualified for the competition, it was against Lens, and Arteta's inexperienced team lost even though they had taken the lead. This time, though, they scored a second goal right away.
Early in the second half, Martin Odegaard, who had been quiet hitherto, struck the crossbar. However, Jesus dribbled into the box from the left wing and skillfully fired a shot across Nyland into the far top corner.
Just before the hour, Nemanja Gudelj, walking by the unmoving Raya on his way home from Ivan Rakitic's corner, gave Sevilla a response.
Mariano Diaz's attempt was tipped over the crossbar by the amazing Arsenal goalie; had it gone through, it would have been called back for a foul.
Despite Erik Lamela, a former Tottenham winger, being booked for diving in the area, Sevilla persevered and defeated both Manchester United and Juventus at home during their Europa League run last season.
In the last moments, they flipped the script, but Arsenal held on to win.