Couture fashion designer Tarun Tahiliani, called the Oscar de la Renta of India, distills historical themes into modern, luxurious rugs like none we’ve ever seen.

Some sell for $3,000 or $4,000, whereas Azimzadeh has a 2,000 square meter traditional carpet from Tabriz priced at $120 million. His inventory also holds a 170-year-old piece from Kashan ...