How did Islam become so prevalent and entrenched in Indian society during this period?

Well, Islam arrived in India since ancient years.

India was located exactly next to Pakistan, and since the 7th century, Indian and Middle East countries has been partners in trading a lot of commodities such as oil, gold, silk, etc

Over the Centuries, The muslim culture has been integrated with indian Hindu Culture, and the muslims have played prominent roles in India's economic rise ever since