Fresh from an Arkansas state championship at Pine Bluff High School, Reed joined the Arkansas men's basketball team in 1977, at the height of the success of the "Triplets" – Sidney Moncrief, Ron Brewer and Marvin Delph – and was a key part of the team that made it to the 1978 NCAA Final Four, finishing third after losing to eventual champion Kentucky Wildcats in the semifinal game. A guard, Reed broke into the starting line-up for the Razorbacks in his sophomore year and was a starter for the remainder of his career. In 1979, Reed was instrumental in helping Arkansas to a very successful season following the loss of Brewer and Delph. The team, captained by Moncrief, made it to the NCAA Regional Finals before losing to the Larry Bird-led Indiana State Sycamores. In the game, Reed was called for traveling after he tripped with 1:02 remaining in the game, and the Sycamores held on for the final shot. Sycamore player Bob Heaton took five steps to the bucket and scored on a left-handed shot at the buzzer, giving ISU a 73–71 win and a trip to the Final Four, where they finished second to Magic Johnson and the Michigan State Spartans. Following that season, Reed played as a member of the gold medal-winning American team at the 1979 World University Games, joining such teammates as Kevin McHale, Jeff Ruland and Andrew Toney. The 1981 NCAA Tournament featured the shot that turned Reed into a star of the NCAA tournament. In the second round of the tournament, the Southwest Conference champion Razorbacks were playing the defending NCAA tournament champion Louisville Cardinals in Austin, Texas. Trailing by one with five seconds remaining in the contest, the Razorbacks threw the ball to Reed after a timeout. He was unable to get the ball to any of his teammates, including future NBA players Darrell Walker and Scott Hastings, and took a desperation shot from just beyond the mid-court line as the clock expired. The ball ripped through the net, giving Arkansas a 74-73 victory. The team lost their next game against the LSU Tigers. Reed ranks number 21 on the Arkansas all-time scoring list at the start of the 2008–2009 season with 1,260 points. Only 6 foot 2 inches tall, he led the Razorbacks in blocked shots in 1979 with 30. A member of three Southwest Conference championship teams, Reed ended up playing in four NCAA Tournaments during his tenure and was named National Association of Basketball Coaches All-District in 1980 and 1981.