Level at 1-1 after the first leg - salvaged late by a Kai Havertz penalty in Germany - Arsenal approached the return fixture with greater control and urgency, never allowing their opponents to settle. The hosts dictated the tempo early, repeatedly testing goalkeeper Janis Blaswich, who was forced into a string of saves to keep the tie balanced.
Gabriel Magalhaes twice threatened from set-pieces, while Leandro Trossard and Bukayo Saka combined to probe a well-organised Leverkusen defence. Despite the pressure, the breakthrough required something special - and it arrived 10 minutes before half-time.
Collecting a pass on the edge of the area, Eze took a touch to steady himself before swivelling and unleashing a powerful strike into the top corner, leaving Blaswich with no chance. It was the 27-year-old's first Champions League goal and a decisive moment in the tie.
Arsenal maintained their dominance after the break, continuing to press forward with intent. Their control was eventually rewarded just after the hour mark when Declan Rice reacted quickest to a loose clearance, driving forward before calmly placing his finish beyond the goalkeeper to double the lead and effectively end the contest.
Leverkusen offered little in response, though David Raya was required to produce a sharp save late on to deny Christian Kofane a consolation.
The visitors were largely kept at arm's length throughout, with Blaswich's performance ultimately preventing a heavier defeat as Arsenal created chances in waves. Ben White also came close during a first-half scramble, underlining the hosts' sustained pressure.
The result sealed a 3-1 aggregate win and ensured progression to the last eight, where Arsenal will face Sporting CP, who advanced after a dramatic turnaround in their own tie earlier in the evening.