Eze's fine whipped finish from 20 yards gave goalkeeper Nick Pope no chance and put the title-chasing hosts ahead early on at the Emirates Stadium.
The Magpies had started well and threatened inside the opening 20 seconds when ex-Gunner Joe Willock - one of five players brought into the side by Eddie Howe following last weekend's defeat to Bournemouth - burst through the middle and played in Will Osula, who missed his kick.
Skipper Bruno Guimarães, recently back from injury and in the starting line-up for the first time since February, then lashed just over from the edge of the box after picking up Sandro Tonali's pass.
At the other end, Eze lashed just wide following a short corner before another similar routine saw Kai Havertz give the England international another shooting opportunity from the edge of the box, which he dispatched with aplomb.
**Newcastle United:** Nick Pope, Sven Botman, Sandro Tonali, Malick Thiaw, Will Osula, Jacob Murphy, Joe Willock, Dan Burn, Bruno Guimarães (c), Jacob Ramsey, Lewis Miley
**Substitutes:** Aaron Ramsdale, Kieran Trippier, Lewis Hall, Yoane Wissa, Harvey Barnes, Anthony Elanga, Nick Woltemade, Alex Murphy, Sean Neave