A native of Massachusetts, Shea found himself in the closer role during his first big league season with Houston in 1968. He registered a 4-4 record with six saves and a 3.38 ERA in 30 games. Sold to the expansion Montreal Expos in the off-season, he appeared in 10 games for Montreal in 1969, posting a 2.87 ERA with no record. That was the extent of his big league career.

Shea passed away on March 4, 2015 in North Hampton, NH at age 72.