He painted for many years out of his studio in the Old University Building of New York University.
Painting in the Adirondack Mountains and later in Waterford, Connecticut, Minor soon became known for his landscapes resembling the Barbizon School.
Under the influence of George Inness and Alexander Helwig Wyant, he also began to paint in a Tonalist style.
His painting Great Silas at Night (1897) displays his adoption of the Tonalist style while his lingering Barbizon style can be seen in A Hillside Pasture.
From the 1890s until his death, Minor exhibited frequently with the Tonalists in New York.
In 1897, he was elected a member of the National Academy of Design, New York.
In 1900, Minor achieved the height of his success at the historic William T.
Evans sale in 1900, where his painting The Close of Day (private collection) fetched $3,050, the highest price for a landscape by a living American painter at that auction.
Over the course of his lifetime, Minor was a member of the Society of American Artists and the Salmagundi Club.
He exhibited in New York, Brooklyn, Chicago, and elsewhere in the United States, as well as in the Royal Academy of London and the salons of Paris and Antwerp.
Minor was plagued with bad health during the last decade of his life, decreasing the quantity and likely the quality of his works.
He died at his home in Waterford, Connecticut, on 4 August 1904.
His paintings are owned by the Smithsonian American Art Museum, the Yale University Art Gallery, the Mead Art Museum, the Lyman Allyn Museum, the Florence Griswold Museum, the Brooklyn Museum, the Newark Museum, the Robert Hull Fleming Museum, the Haggin Museum, the Salmagundi Club, the Memorial Art Gallery, and the University of Arizona Museum of Art.