Tusker came from a goal down to knock out Bandari following a dramatic 2-1 victory at the Mbaraki Stadium.
Wycliffe Ochomo gave Bandari the lead in the fourth minute, but the visitors scored twice in either half to progress to the next round.
Timothy Otieno brought Tusker back to the game with a late first-half equalizer before the visitors completed the job in the second stanza.
Bandari blew a chance to double their advantage from the spot. The home side were awarded a penalty, but captain Felly Mulumba was denied by the crossbar.
Boniface Muchiri spared the two sides the agony of a replay when he scored the match-winner late in the second half.
The win over Bandari could not have come at a better time for Tusker who were knocked out of the same competition by the same side in the last edition at Kinoru Stadium.
The 2017 losing finalist Kariobangi Sharks also sailed to the round of 16 with a 4-2 victory against Wazito.
Sharks needed a post-match penalty to progress to the next stage, but Wazito dug from the Super Cup experience to down Wazito after both sides played to a 2-2 draw in the regulation time.
Mwatate United got a bye into the second round after Ushuru failed to honor the match. The tax collectors failed to travel to Taita Taveta to honor the fixture citing lack of funds.
The National Super League side were scheduled to play Mwatate United at the Wundanyi Stadium.
The joined Kakamega Homeboys who failed to honor their round of 32 matches against Ulinzi Stars on Wednesday, citing poor communication from Football Kenya Federating.
Elsewhere, Leysa FC booked their maiden appearance in the round of 16 after upsetting FKF National Super League side KCB 2-1.
Dennis Maina powered in a strike that saw Leysa before the victors cut their lead via an own goal scored by Harry Gentle.
Justus Anene made amends for the Laysa when he sent a powerful drive past Juma Mpongo in the KCB goal deep in stoppage time to help his side knock out the former KPL side.
Posta Rangers also sailed through to the next round after a 1-0 victory over Division One side Kisumu Hotstars.
Sunday Fixtures: Vegpro vs Vihiga United (Karuturi Grounds, 1 pm), Rainforest vs AFC Leopards (Karuturi Grounds, 3.15 pm), Friend Zone vs Zetech University (Camp Toyoyo, 11 am), Sofapaka vs Baba Dogo United (Camp Toyoyo, 1 pm), Kenya Police vs Nzoia Sugar (Narok Stadium, 3 pm), Western Stima vs Bidco United (Moi Stadium Kisumu, 3 pm), Bungoma Superstars vs Transfoc (Kanduyi Stadium, 3 pm).