Persian دولبند dūlband "turban" was borrowed into Turkish as tulbant/tuliband, then found its way into Italian as tolipante, making its way into English as turban. It is not known exactly when the change of tul- to tur- took place.
The Turkish word was borrowed again as modern Latin tulīpa, Italian tulipano, French tulipan, tulipe, English tulip. According to the OED, the tulip was introduced into Europe from Turkey in the 16th century. It was so called because of its likeness to the turban in shape.
According to Yule, the dūl- of dūlband is from Arabic dul "to roll". I wonder if the -band is from Proto-Indo-Iranian bandh- as in Hindi bāndhanā "to tie" and bandanna.