He was a graduate from Magdalene College, Cambridge, and emigrated to the Thirteen British Colonies as a minister, following disagreements with Archbishop Laud.
At the convention of 4 June 1639 (O. S.) Eaton took exception to the fifth article of the constitution, which limited the right of voting and of holding public office to church members only on the ground that "the free planters ought not to surrender this power out of their hands".
He was afterwards chosen teacher of a congregational church at Dukinfield in Cheshire, whence he removed to the neighbouring borough of Stockport, where he preached in the free school.
Upon being silenced in 1662 he attended the ministry of John Angier at Denton, near Manchester, where, it is said, many of his old hearers who had disliked him much while he was their minister "were wrought into a better temper".
In his funeral sermon he is stated to have suffered not only from the persecution which raged against the silenced ministers, being "several times brought into trouble and imprisoned", but from grievous bodily affliction; he had "been dying many years".
Eaton's writings were favourably regarded by the council of state, who, convinced of his "merit and good affection", augmented his stipend on two occasions (ib.