Baker had served in the Union Army during the American Civil War, rising to the rank of colonel, but resigned following his election as lieutenant governor, during which time he played an important role in overseeing the formation and training of states levies.

During Baker's full term as governor, he focused primitively on the creation and improvement of institutions to help veterans and their families that had been disaffected by the war.

His brother, William Baker, had also become active in the local politics, and served four terms as major of Evansville during the same time period.

[3] Baker left the army in 1864 to run again as Lieutenant Governor on the ticket with Oliver Morton and was elected with a 20,000-vote majority.

[3] In 1868, Baker was reelected to the position of governor, defeating Thomas Hendricks by 961 votes, the closest in state history.

During his administration, a women's prison was built, and a soldiers' home to assist the returning veterans and the Indiana State Normal School in Terre Haute were constructed.

Baker then hired painters and sought out the families of the former governors to procure photos and paintings from which official portraits could be created.

[5] Baker's most difficult goal to achieve was the ratification of the post-war amendments that, among other things, banned slavery and granted blacks the right to vote.

The Democrats had resigned office en masse when the bill was put up for a vote to deny quorum, but the Republicans went ahead to approve the amendment.

When the Democrats took the legislature in the following election, they revoked the ratification of the amendments, but it was too late and the federal government, which was Republican-dominated at the time, had already added them to the constitution.

After Hendricks was elected governor in 1872, Baker took on state attorney general Oscar B. Hord and Chief Justice of the Indiana Supreme Court Samuel Perkins as partners.

Baker remained active in public affairs and urged the state schools to grant equal opportunities.