The lower league side prevailed 5-4 after a penalty kicks shootout, following a 1-1 draw at full-time.
Kalu Nweke opened scoring for Kwara United in the 23rd minute of the match played at the Nnamdi Azikiwe Stadium.
Jide Williams’ own goal however drew the game level in the 88th minute.
The match then went into a penalty kicks shootout, from which Kebbi United overcame Kwara United 5-4 to progress.
In the competition’s Round of 16, they will meet Kano Pillars on Wednesday in Minna.
Speaking after the match, Kwara United’s coach, Abdullahi Bigfoot, said his team gave the match away due to lack of concentration.
“That is a Cup competition for you. It was a 90-minute game in which we missed lots of chances and it came back to haunt us.
“I do not have an answer to the own goal we conceded because we were not under pressure.
“Now we are going to place all our concentration on the NPFL to ensure we finish well as we are now out of the AITEO Cup Competition,” he said.
Kebbi United’s goalkeeper Yasha’u Yusuf, on his part, said they were underrated by their opponents and it had now turned out to be a blessing.
“We know we are the underdogs and that was why we put in all our efforts to win or lose gallantly,” he said.
Yusuf went on to disclose that stopping penalty kicks had been his speciality and he was not surprised that he showed the stuff he was made of in the match.
“Our opponents underrated us but we did not underrate ourselves and the result is the reward for our self-belief.
“Kebbi United’s target in the ongoing AITEO Cup Competition now is nothing but reaching the final and probably lifting the trophy,” he said.