Veteran playmaker Siyabonga Nkosi netted with a powerful strike in the 27th minute at the National Stadium in Gaborone, Botswana.
The Glamour Boys won the first leg of the preliminary round tie 2-1 in Johannesburg on February 14.
Chiefs entered the return duel without injured midfielder George Maluleka and striker Siphelele Mthembu, as well as Reneilwe Letsholonyane, who is on compassionate leave following the death of his father.
Amakhosi started brightly, as Bernard Parker forced a low save from goalkeeper Mwampule Masule, while Siphiwe Tshabalala had a penalty shout turned down early on.
Stuart Baxter's men made their dominance count when Nkosi thundered in the opener, with the hosts unable to make much of an impression before the interval.
Rollers showed more intent in the second stanza as Chiefs' central defensive pairing Tefu Mashamaite and Mulomowadau Mathoho endured some anxious moments, particularly on set-pieces.
However, Baxter's unit held firm to progress.
Rollers: Masule, Mooketsi, Mathumo, Ncenga, Moswate, Majawa, Ditshupo, Kebaikanye, Boy, Sikele, Louis. Subs: Bolweleng, Molemogi, Koko, Ngwenya, Ngele, Kaekwe, Pepukani.
Chiefs: Khuzwayo, Mashamaite, Gaxa, Masilela, Mathoho, Katsande, Nkosi, Tshabalala, Rusike, Masango, Parker. Subs: Pieterse, Mphela, Lebese, Moleko, Gould, Ekstein, Bukenya.