Myrlie Evers, widow of slain civil rights leader Medgar Evers, was confirmed Friday by the Los Angeles City Council as a public works commissioner--24 years to the day that her husband was assassinated. Evers, a former community relations executive for Arco and an unsuccessful candidate in the recent 10th Council District race, was appointed to the $60,400-a-year post to succeed Homer F. Broome Jr. The term ends June 30, 1988. Broome had resigned the post to run for the 10th District race, finishing as runner-up to new Councilman Nate Holden. Evers is a national director of the NAACP.