Step 1: Read the question.
We must find who defeated the rulers of the Qutub Shahi dynasty.
Step 2: Who the Qutub Shahis were.
The Qutub Shahi dynasty ruled the Golconda kingdom in the Deccan, with capitals at Golconda and later Hyderabad.
Step 3: The Mughal expansion.
The powerful Mughal emperor Aurangzeb wanted to spread his empire into the Deccan and bring Golconda under his control.
Step 4: The defeat.
In 1687 Aurangzeb's forces captured Golconda and ended the Qutub Shahi rule.
Step 5: Rule out the others.
The Asaf Jahis came to power later, after the Mughals. The Kakatiyas and Vijayanagara rulers belonged to earlier times, not the fall of the Qutub Shahis.
Step 6: Conclude.
The Qutub Shahi rulers were defeated by Aurangzeb.
\[ \boxed{\text{Aurangzeb}} \]