Maxwell was a native of Clarinda, Iowa. During the 1930s, she worked as an usher in Fort Wayne, Indiana at the Rialto Theater located at 2616 South Calhoun Street.
She started her professional entertaining career as a radio singer while still a teenager, before signing with Metro-Goldwyn-Mayer in 1942 as a contract player. Among the programs in which she appeared were Beat the Band and The Abbott and Costello Show. The head of MGM, Louis B. Mayer, insisted she change the "Marvel" part of her real name. She dropped her first name and kept the middle one. Some of her film roles included Lost in a Harem (1944), Champion (1949), The Lemon Drop Kid (1951), and Rock-A-Bye Baby (1958). The song "Silver Bells" made its debut in The Lemon Drop Kid, sung by Maxwell and Hope.
Maxwell married three times; each ended in divorce. In September 1944, she married actor John Conte; the relationship was dissolved in June 1946. Her second marriage, to restaurateur Anders McIntyre, lasted just over a year, from January 1, 1950 until March 23, 1951. Maxwell's six-year marriage to writer/producer Jerry Davis ended in 1960. Her only child, Matthew, was born to Maxwell and Davis in 1956.
Maxwell appeared twice as a singer in the second season (1955–56) of NBC's The Jimmy Durante Show. On May 16, 1957, she guest-starred on NBC's The Ford Show, Starring Tennessee Ernie Ford.
In the 1961–62 television season, Maxwell played Grace Sherwood, owner of the diner on ABC's 26-episode Bus Stop, a drama about travelers passing through the fictitious town of Sunrise, Colorado. She left the series after 13 episodes, saying, "There was nothing for me to do but pour a second cup of coffee and point the way to the men's room."
On March 20, 1972, at age 50, Maxwell was found dead in her home by her 15-year-old son, who had arrived home from school. The cause was an apparent heart attack; she had been treated for hypertension and pulmonary disease. Bob Hope, Bing Crosby, Frank Sinatra, and Jack Benny were honorary pallbearers at her funeral.
Maxwell also had a multi-year affair with Frank Sinatra, as detailed in Alex Gibney's 2015 documentary on Sinatra for HBO, All or Nothing At All.
