Davenport was born in Canton and grew up in Philadelphia. He came from a long line of stage actors; his father was the famed thespian Edward Loomis Davenport and his mother, Fanny Vining, was an English actress descendant of the renowned 18th-century Irish stage actor, Jack Johnson. His sister was actress Fanny Davenport. He made his stage debut at the age of five in the playDamon and Pythias
He started his film career at the age of 48. His film debut came in 1914 with silent film Too Many Husbands, in which he played a man trying to keep his love-struck nephew away from a young woman he had raised as his daughter. Later that same year, he starred inFogg's Millions co-starring Rose Tapley. The film would go on to become the first in a series of silent comedy shorts. In addition, he also directed eleven silent features during the pre-World War I era, including many of the films in the Mr. and Mrs. Jarr series.
In 1913, he co-founded, along with actor Eddie Foy, the Actors Equity Association, an American labor union for actors. The original organization, known as The White Rats, was spearheaded by Davenport. After a nine month stretch, the actors' group united in defiance of the appalling treatment of actors by theater owners such as the Shubert family andDavid Belasco, among others, by refusing to appear on stage by striking. The actions of the association caused the closure of all the theaters on Broadway, the only exception being theaters owned by George M. Cohan's company.
Some of the most famous films that he appeared in are The Bride Came C.O.D., filmed on location in Death Valley, The Life of Emile Zola, You Can't Take it With You, Gone with the Wind, The Hunchback of Notre Dame, Foreign Correspondent, Kings Row, The Ox-Bow Incident, The Bachelor and the Bobby-Soxer, and Meet Me in St. Louis.
He married Alice Davenport in 1893. They had one daughter, Dorothy Davenport, who also became an actress. After divorcing Alice in 1896, he married actress Phyllis Rankin, that same year. They had four children, all actors: Arthur Rankin (father of Arthur Rankin, Jr., founder of the Rankin/Bass animation studio), Ned Davenport, Ann Davenport, and Kate Davenport. The 10 August 1949 Canton Sunday Telegram obituary noted that the couple were together until her death, contrary to reports that he divorced her and re-married. Through his marriage to Phyllis, he was the brother-in-law of Lionel Barrymore, who was married at the time to Phyllis' sister Doris. Phyllis's father, McKee Rankin, had been the top actor at the Arch Street Theater, which was run by Lionel's grandmother and Sidney's mother, Louisa Lane Drew. He was the grandfather of producer Dirk Wayne Summers,Arthur Rankin Jr. and Wallace Reid Jr.
After Phyllis's death, Davenport moved to Los Angeles and lived with his now-grown children. He died of a heart attack at the age of 83.