In 1608 he succeeded to the rectory of Burton-Latimer and was appointed chaplain to Prince Charles.
Owen was in favour with William Laud, and was liked by Charles I; on 18 August 1629, he was elected bishop of St Asaph.
He was active in the pastoral work of his bishopric and was the first to institute a series of Welsh sermons to be preached in the parish church the first Sunday of each month by members of the parish who derived a portion of their income from its tithes.
He superintended improvements in the structure of the cathedral, including the building of a new organ in 1635.
Having joined in the petition of the eleven bishops on 30 December 1641, he was impeached of high treason and imprisoned in the Tower of London.
He was deprived of his See by Parliament on 9 October 1646, as episcopacy was abolished for the duration of the Commonwealth and the Protectorate.