There was a concern for Saka as he limped off the pitch with an injury later in the second half.
The result leaves Newcastle winless after 13 league games and rooted to the bottom of the table.
The hosts should have taken the lead just before the break but Arsenal captain Pierre-Emerick Aubameyang missed a sitter from close range as scores remained level at half time.
Arsenal did open the scoring after 55 minutes after Saka rounded off a stunning team move and calmly slotted the ball into the far corner.
Substitute Martinelli doubled Arsenal’s lead with his second touch 10 minutes later with a smart first-time finish.
The visitors attempted to make a comeback but remain without a win as Eddie Howe watched on for the first time in the dugout after recovering from COVID-19.