1580s, "to rule in a despotic or arrogant manner," from Dutch domineren "to rule, play the master; to feast" (16c.), from Middle French dominer, from Latin dominari "to rule, 'lord' it over," from dominus "lord, master," literally "master of the house," from domus "house, home" (from PIE root *dem- "house, household") + -nus, suffix denoting ownership or relation.
Shakespeare's usage ("Taming of the Shrew") is not the earliest in English. Meaning "give orders or directions in an arrogant, blustering manner" is from 1764. Related: Domineering; domineeringly.