Eze opened the scoring in the 36th minute with a powerful effort from the edge of the area, registering his first goal in the competition, before Declan Rice added a second after the break to seal the result.
Arsenal dominated much of the tie but had been frustrated before Eze's intervention, with Arteta highlighting the importance of the breakthrough.
"We needed a magical moment and that's what he produced," Arteta said. "That's the reason why he's here."
The goal caps an upturn in form for Eze following a slow start to his first season after joining from Crystal Palace. Arteta said the midfielder's recent run of games has been key to his improvement.
"He's playing every three days, he has rhythm and a better understanding with his team-mates," he said. "You can see his consistency now."
Rice's second-half finish ensured Arsenal's control was reflected on the scoreboard, with the England midfielder also drawing praise from his manager.
"In the second half, Declan's action gave us the opportunity to win the game," Arteta said. "He was immense."
The victory extends Arsenal's strong run in Europe this season and sets up a quarter-final against Sporting CP.
Despite the comfortable progression, Arteta said his side could have scored more, pointing to several missed chances across the two legs.
Arsenal now turn their attention to domestic competition, with a cup final approaching as they continue to compete on multiple fronts.