After playing basketball at the College of the Holy Cross during the late 1950s and early 1960s, the 6'1" Blaney spent one season with the New York Knicks of the National Basketball Association. In 1967-68 he served as head coach at Stonehill College and Dartmouth College 1969-1971. From 1972 to 1994, he served as head coach of Holy Cross, compiling a 357-276 overall record. He then became head coach at Seton Hall University, where he led the team to the NIT twice before being fired following the 1996-97 season. In 2000, he began serving as an assistant head coach at the University of Connecticut.
Blaney, while filling in for Jim Calhoun, made history at UConn on January 23, 2010 when UConn defeated the No. 1 ranked University of Texas Longhorns 88-74. It marked the first time that an opponent had come to Gampel Pavilion ranked first in the nation, and was subsequently the first time UConn ousted the nation's top team at home.
Blaney also filled in for Calhoun for 11 games in the 2011-12 season. He is credited with the first three games of the 2011-12 Big East Conference season, when Calhoun sat out a conference-imposed suspension for recruiting violations. He also served as interim coach throughout February 2012, when Calhoun went on medical leave; those eight games, however, are credited to Calhoun.
Blaney announced his retirement on June 13, 2013.