[1] Following stage success in Hollywood, McVeagh moved to New York City in her 20s, performing on radio and on Broadway in several productions including the roles of Martha in Snafu (1944–1945)[4] and Patsy Laverne in Too Hot for Maneuvers (1945).

The production received very favorable reviews on the West Coast and was en route to New York where it was predicted to be the "comedy smash hit of 1948".

Her stage career continued in Las Vegas in 1981 in The Ninety Day Mistress, playing the mother of June Wilkinson's character.

[1] McVeagh's first film appearance was a supporting role in the classic High Noon (1952) in which she played Mildred Fuller alongside Gary Cooper and Grace Kelly.

During that time, she co-starred in Tight Spot as Clara Moran playing the sister of Ginger Rogers: Of her performance, The New York Times raved "For our money, the best scene, whipped up by scenarist William Bowers, is the anything-but-tender reunion of Miss Rogers and her sister, Eve McVeagh ... an ugly, blistering pip.

She starred as Viv in The Glass Web, and was featured as Mrs. Clinton in Three in the Attic, Mrs. Masters in The Way West, Mrs. Griggs in Crime & Punishment, USA, a reporter in the Dino De Laurentiis production of King Kong, and The Graduate.

Ms. McVeagh's contributions to film were recognized by the bestowal of full voting membership in the actor's branch of the Academy of Motion Picture Arts and Sciences in September 1974.

[citation needed] McVeagh's career in television began in 1946 as a primary cast member in the first American network Soap Opera, Faraway Hill.

She rounded out the 1970s on a high note as socialite Helen Carrington in the 1979 critically acclaimed television movie Murder by Natural Causes with Hal Holbrook.

McVeagh guest starred in a 1985 episode of Cagney and Lacey as Dorothy Gantney, the grief-stricken mother of a murder victim in "The Psychic".

[1] McVeagh was married to character actor and director Clarke Gordon (her fourth husband) at the time of her death and had four children and nine grandchildren.