Itumeleng Khune returned in goal for the Soweto giants, while Khama Billiat started on the bench as Reeve Frosler slotted in at right back ahead of Kgotso Moleko.
Chiefs were on the back foot after two minutes, but Khune got down to gather Siphesihle Msomi's low shot following a cross from the left.
The Amakhosi quickly got into gear and opened up the visitors on the far side, but Lebogang Manyama's cross-field ball failed to connect with Samir Nurkovic and Leonardo Castro.
George Maluleka went close to giving the Chiefs the lead with a pile-driver outside the area after 16 minutes, but Edward Maova tipped the effort for a corner.
Eagles were on the charge following the half-hour mark as Msomi worked space around the area before firing wide of the near post.
Chiefs threatened at the other end though as Nurkovic guided wide from the far post following a cross from the left as the hosts endured a frustrating first half.
Billiat came on at the start of the second half along with Bernard Parker, as Ernst Middendorp refreshed his stall. The Zimbabwean's introduction proved telling as he brought down a long ball to set up Manyama for a shot in the area, but strong goalkeeping from Maova denied the latter minutes in.
The Zimbabwean was then at the end of two clear misses four minutes of each other as he failed to punish a defensive error whilst volleying a cross into the area wide of the near post.
The Amakhosi' frustrations in front of goal came to an end after 70 minutes as Manyama lobbed into the top corner after showing good footwork in the area.
Anthony Akumu Agay, who joined in January, made his debut for the hosts after replacing Maluleka in the last five minutes.
Eagles looked to send the game into extra time in the latter stages, but the Amakhosi ensured progression to the last 16.
Chiefs: Khune, Frosler, Ntiya-Ntiya, Cardoso, Mathoho, Katsande, Maluleka, Baccus, Castro, Manyama, Nurkovic.
Subs: Akpeyi, Parker, Mphahlele, Billiat, Akumu, Sasman, Mashiane.
Eagles: Maova, Kalake, Klaas, Tema, Mashau, Msomi, Ntsundwana, Mdluli, Seanego, Hlongwa, Maruping.
Subs: Dlamini, Kizza, Zikalala, Matima, Ntswane, Maluleke, Mongae.