Babur.
Inherited lands in Afghanistan and Transoxania that were what was left from his grandfather (IIRC) Tamerlane - a man perhaps more brutal then Genghis, and a fanatical Muslim.
Babur decided that fighting his traditional enemy the Uzbeks over pats of Tamerlane's old empire wasn't worth it and expanded instead into northern India, which was wealthy but ruled by a weak and incompetent line of sultans.
After winning the battle of Panipat against serious odds, Babur became the ruler of northern India.
Timur-e-Lang was not Babur's grandfather, but his ancestor and Babur was one of the Timurid princes in line to take over Samerkhand.