Jesus scored twice and claimed two assists too, with Granit Xhaka and Martinelli also getting on the scoresheet at Emirates Stadium.
This was a dominant performance from Arsenal, but Leicester did twice peg them back through a William Saliba own-goal and James Maddison.
Mikel Arteta’s side, however, were worthy winners and have now won both of their opening Premier League games this season.
Simon Collings was at Emirates Stadium to see Arsenal in action...
Aaron Ramsdale 5
Made a big save early on to deny Wesley Fofana, but will be disappointed with the mix-up for the own-goal. Was also beaten too easily by Maddison from a tight angle.
Ben White 7
Will be a bit disappointed with the first Leicester goal as James Justin beat him in the air for the flick on. Other than that, he did well, making a huge tackle to stop Patson Daka scoring.
William Saliba 6
The own-goal was the only bad note on an otherwise good afternoon for the Frenchman. Given he is still only 21, mistakes will happen along the way.
Had a better game than he did at Crystal Palace last week, where he was a tad shaky at times. Dealt well with the threat of Jamie Vardy.
Oleksandr Zinchenko 8
Looked excellent on his home debut and exactly what you’d expect from a player signed from Manchester City. So good in possession, especially when he tucks inside to join the midfield.
Martin Odegaard 7
There were a couple of lovely touches from the Arsenal captain, particularly around the Leicester box as he tried to open them up.
Thomas Partey 7
Looked assured and solid at the base of the Gunners’ midfield. Broke up play well and grew into the game with some decent passing.
Granit Xhaka 9
Had an excellent game in midfield and was a contender for man of the match. Scored and could have had another, but he hit the post. Playing some of his best football for Arsenal right now.
Bukayo Saka 7
The quietest of Arsenal’s forwards but he still had a good game. Created some great chances with his crossing, one of which Xhaka smashed against the post.
Gabriel Jesus 9 | Star player
What a home debut from the Brazilian. He scored twice, taking his first brilliantly, and should have had a hat-trick. Got two assists too.
Gabriel Martinelli 9
Looked super bright and lively out wide, linking up well with Jesus on numerous occasions. Gave Fofana a tough afternoon and got the goal his performance deserved.
Takehiro Tomiyasu (White 75’) N/A
Kieran Tierney (Zinchenko 77’) N/A
Emile Smith Rowe (Saka 84’) N/A
Eddie Nketiah (Jesus 84’) N/A
Subs not used: Turner, Holding, Pepe, Sambi Lokonga, Elneny.