Arsenal boss Mikel Arteta was able to exhibit the strength in depth of his squad as Eze, Bukayo Saka and Gabriel Martinelli were among the nine changes from Sunday’s 1-1 draw against Manchester City.
Eze has made an impressive start after his move from Crystal Palace last month that could be worth up to US$92 million.
The England international slotted in from Myles Lewis-Skelly’s flick to give Arsenal the perfect start after just eight minutes.
“I’ve been waiting to score for this club for a long time and the first is very special,” said Eze, who was released by Arsenal as a teenager.
The visitors were unable to build on that advantage despite dominating the game.
Devante Cole, son of former Manchester United striker Andy Cole, came closest to a shock equaliser for Vale when his strike flew just over the bar.
Leandro Trossard finally killed the tie off with a powerful and precise finish into the bottom corner five minutes from time.
Arsenal will host Brighton in the next round.
Meanwhile, Phil Foden was City’s key man with a goal and assist as they beat Huddersfield 2-0.
Foden has shown signs in recent weeks of rediscovering the form that made him the Premier League player of the year two seasons ago.
The England midfielder arrowed in a low drive to give the visitors the lead after 18 minutes.
Erling Haaland was among those given the night off as Pep Guardiola made nine changes.
The Norwegian’s lethal finishing was missed as City had to wait until 15 minutes from time to make the tie safe when Savinho blasted in Foden’s pass from a narrow angle.
City’s reward is a trip to second-tier Swansea in the last 16.
Holders Newcastle will face Tottenham in the next round after both cruised to victory against third-tier opposition.
Joelinton and William Osula both struck twice as Newcastle beat League One leaders Bradford 4-1.
Tottenham also got the job done inside the opening 20 minutes in a 3-0 victory over Doncaster. (AFP)
