The fight which was on the Tony Harrison-Jermell Charlo undercard, saw Kiladze’s trainer threw in the towel following a barrage of punches.
Referee Thomas Taylor was forced to stop their scheduled 10-rounder at 2:09 of the fifth round.
The win saw Ajagba take his record to 12 wins, no defeats and 10 coming via knockouts.
In the third-round Ajagba was surprisingly knocked down by the 33-year-old Kiladze.
But after beating the count, an accurate left jab from Ajagba was followed by a powerful right hook, sending Kiladze to the floor and ending the fight.
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