The cause was complications of Parkinson’s disease, said his sister, Susan Jennings, his only immediate survivor.
Jennings played for the Giants for 11 seasons, from 1974 to 1984, during which they went 56-104, had a winning record only twice and never had more than nine victories in a season.
Punters on bad football teams get a lot of work, and Jennings was up to the challenge. Known for kicks that lingered in the air, angled toward the sideline and regularly pinned opposing teams inside their 20-yard line, he was named to four Pro Bowls. The Associated Press named him its All-Pro punter in 1979, when he led the N.F.L. in punts (104) and punting yardage (4,445), and again in 1980, probably his best season, when he led all punters with a 44.8-yard average. He punted 931 times for the Giants, more than anyone before or since, averaging 41.7 yards per kick.
He finished his career on the field with the Jets, playing with them from 1985 to 1987. Over all, his punts traveled 47,567 yards, more than 27 miles, the 11th-highest total in N.F.L. history.
David Tuthill Jennings was born in Manhattan on June 8, 1952. His mother, the former Deborah Hunt, was a pianist and music teacher. His father, Manson, was a college professor and administrator who became president of Southern Connecticut State College (now Southern Connecticut State University).
Jennings played basketball, not football, at Garden City High School on Long Island — basketball was his favorite sport — and both sports at St. Lawrence University, a liberal arts school in northern New York that rarely turns out professional athletes. Undrafted out of college, he joined the Giants after being cut by the Houston Oilers.
Jennings was a presence in New York City football for more than 30 years, though after the Giants moved to a stadium in the Meadowlands in 1976 — the Jets joined them there in 1984 — he played his home games in New Jersey. Personable, articulate and well-informed about the game, he moved from the field to the broadcast booth as an analyst on radio for the Jets from 1988 to 2001 and the Giants from 2002 to 2007.
“You go in there, go ‘boom,’ and then you’re back on the sidelines and you can wait another half-hour before you’re in the game again,” Jennings said in a 1976 interview, describing the punter’s role and expressing disappointment that he wasn’t talented enough to play his favorite sport for a living. “It’s not like basketball, where you’re in the action all the time.”
He added, “I happen to be a better punter than a basketball player.”