Hennessey came to Holy Cross after being All-State for two years at Brookline High School, and he made an immediate impact. In his first game on the varsity squad in 1960, he ran back the opening kickoff 85 yards in the season opener against Harvard. He topped the effort later in the season with an 89 yard return for a touchdown versus Connecticut. That season he set school single-season records by averaging 30.8 yards per kickoff return and returning two kickoffs for touchdowns.
A senior co-captain in 1962, Hennessey finished his three-year career with 1,157 yards rushing and nine touchdowns; caught 47 passes for 779 yards and three scores; scored 98 points and ran back 29 kicks for 723 yards. He led the Crusaders in rushing in two of his three season with the varsity. His senior year efforts earned him All-East and Catholic All-America honors. In addition, Hennessey was named the 1963 Crusader of the Year.
Following graduation he spent a year on a Jesuit mission in Bagdad, Iraq, and then played two seasons with the Boston Patriots, being named their rookie of the year in 1965. He moved on to a long career within the Boston school system as teacher, coach, headmaster and administrator. Moreover, he was a civic leader in Brookline, Mass., serving nine years on the school committee and six years on the board of selectmen. In 2014, the Cypress Playground at Brookline High School and an endowed scholarship were named in his honor.