Nemanja Gudelj pulled one back after Jesus' goal in the 58th minute, but the Spanish side were unable to find the equaliser they craved.
Instead, Mikel Arteta's side held on to claim the three points that means they are now top of Group B after three games.
Simon Collings was at the Ramon Sanchez-Pizjuan to see Arsenal in action...
David Raya 5
Looked shaky playing out from the back early on and gave the ball away too easily. Made a great save in the second-half that he tipped onto the post, but very nearly punched the ball into his own net in stoppage-time.
Ben White 7
Had a poor game at Chelsea last weekend, but was much better here. Did not get forward as much as he usually does, though.
William Saliba 8
A dominant display at the back from the Frenchman. Felt like he won basically every header and 50-50 all night. A class above, again.
Not as impressive as Saliba, but still a good showing from the Brazilian. Made a couple of big headers and clearances when Arsenal were under pressure.
Takehiro Tomiyasu 8
Deserved to start after a good showing off the bench against Chelsea. Performed really well and looked solid throughout. Should keep his place.
Martin Odegaard 5
Could not get into the game, with Arsenal building much of their play down the left flank. Wasted two good chances in the second-half. Off with just under 20 minutes to go for Kai Havertz.
Pace of game seemed to suit the Italian, who was able to get on the ball much more than at Chelsea last weekend. Finished the game as captain.
Declan Rice 7
Put in a lot of work off the ball defensively. Did not get forward as much as he could have with Jorginho sitting, but did make one great run in the second-half.
Bukayo Saka 6
Suffered from Arsenal mainly playing down the left. Not in the game very much. Restricted to a few pot-shots and crosses.
Gabriel Jesus 9 | Star player
Produced one of the best assists you will see as he setup Martinelli to score. Followed it up with a wonder goal, which he curled into the top corner. A complete performance.
Gabriel Martinelli 7
Squandered a great chance early on when he should have scored. Made up for it just before half-time with a composed finish after rounding the goalkeeper.
Kai Havertz (Odegaard 73') N/A
Eddie Nketiah (Jesus 81') N/A
Leandro Trossard (Saka 81') N/A
Jakub Kiwior (Martinelli 90') N/A
Subs not used: Hein, Ramsdale, Cedric, Zinchenko, Elneny, Vieira, Nelson, Smith Rowe.