Jennings attended Summerville High School, where he was a high school All-American and an All-State wide receiver, while helping his team win 3 Division I-AAAA state championships. He posted 85 receptions for 1,760 yards (20.7 avg.) and 17 touchdowns in his final two seasons.
He also was an All-state first baseman, contributing to the school winning 2 state titles.
Jennings accepted a football scholarship from Clemson University. As a freshman, he was a backup wide receiver and his best game came in the 1985 Independence Bowl against the University of Minnesota, where he had 3 receptions for 41 yards, including his first career touchdown.
He became a starter as a junior and was considered at the time the biggest wide receiver in school history. Playing in run-oriented offenses, he excelled at blocking, after the game against the University of Maryland head coach Danny Ford said "Keith is the best blocking wide receiver I've ever seen". He registered 31 receptions (second on the team) for 475 yards. His best regular season game came against North Carolina State University, when he had 6 receptions for 84 yards. In the 1988 Florida Citrus Bowl, he posted 7 receptions for a school-bowl record 110 yards against Penn State University. The 7 receptions were the most by a Tiger player since 1981.
As a senior, he posted 30 receptions (led the team) for 397 yards and one touchdown, while helping his team win a third straight Atlantic Coast Conference championship.
He finished his career with 78 receptions (eighth in school history) for 1,117 yards (ninth in school history) and 2 touchdowns. During his time in college, his teams had a 34-12-2 record and appeared in 4 bowl games.
Jennings was selected by the Dallas Cowboys in the fifth round (113th overall) of the 1989 NFL Draft, with the intention of converting him into a tight end, even though he didn't have any previous experience at that position. He was released on September 4 and signed to the team's practice squad.
He was promoted to the active roster before the seventh game and went on to appear in 10 games. He played mainly on special teams and as a second tight end in short yardage situations. Against the Green Bay Packers he had 4 receptions for 37 yards. He was waived injured on September 2, 1990.
On July 3, 1991, he was signed as a free agent by the Denver Broncos. He was released on August 26, 1991.
In 1991, he played for the Montreal Machine of the World League of American Football.
On October 18, 1991, Jennings was signed as a free agent to replace Cap Boso who had suffered a career-ending knee injury. With the Chicago Bears he developed into a blocking tight end and by his second season, he was named the starter in place of James Thornton, who was placed on the injured reserve list.
He was released on August 28, 1994 and later re-signed on October 24, after starter Chris Gedney was lost for the season.
In 1995, he recorded the most touchdowns by a Bears tight end (6) since Mike Ditka's finished with 8 in 1963. The following season, he was placed on the injured reserve list with a broken left leg, after the sixth game of the season. He was waived injured on December 10, 1997.
On August 4, 1998, he signed with the Detroit Lions, before being waived on August 30.
With the Las Vegas Outlaws, he served as a reserve tight end during the 2001 season.
His older brother Stanford Jennings played for the Cincinnati Bengals of the National Football League.