It was Thursday, according to:
http://www.Baseball-almanac.com/box-scores/boxscore.php?boxid=197909270BOS
which gives the box score for a baseball game played that day.
Feb 27 1979 was a Tuesday.
July 27, 1979 fell on a Friday.
27 September 1982 was a Monday.
27 September 1948 was a Monday.
September 27 1950 was a Wednesday.
27 September 1918 was a Friday.
27 September 1938 was a Tuesday.
September 27 1962 was a Thursday.
27 September 1958 was a Saturday.
September 27 2010 was a Monday.
September 27, 1969 was a Saturday.
September 27, 2005 was a Tuesday.