Greene played high school basketball at Van Nuys High School, where he was 3A Player of the Year in Southern California in 1982-83. He only began playing organized basketball as a sophomore in high school, and he played sparingly in his first year at New Mexico, averaging 1.4 points in 25 game appearances. He continued developing his skills in a pro-am circuitsummer league in Los Angeles, getting more comfortable as a guard and shooter. The summer league work paid off, and as a sophomore, in 1984-85, Greene became a starter for the Lobos, averaging 11.4 points and 4.3 rebounds a game. Greene shared backcourt duties with fellow sophomore Kelvin Scarborough, and the young Lobo squad went 19-13 with an appearance in the NIT. Four starters were returning for the 1985-86 season, but Greene was injured during a preseason practice and missed the season.
Junior and senior seasons
Greene returned for his junior year in 1986-87 to lead New Mexico with 21.1 points and 6.2 rebounds a game. The team set the Lobo season record for most steals, and Greene set the individual Lobo record for number of steals in a season. Scarborough averaged 18.9 points and six assists and set the Lobo career record for steals. The Lobos beat Texas and Oklahoma State and built a 17-5 record before losing three straight on the road in a strong year for the WAC. They then won eight straight and reached the conference tournament final, missing a last second shot and losing to Wyoming, which would go on to the Sweet Sixteen in the NCAA tournament. The WAC placed three teams in the NCAA, but the Lobos settled for the NIT. They finished the season 25-10, the most wins for a Lobo team up to that time. Greene was a smooth scorer and versatile player who maintained a composed countenance on the court, leading quietly by example. As a senior, he averaged 16.8 points and 6.8 rebounds and again led the team in steals. His most memorable moment came in a game named by a panel of writers as the top game ever at The Pit, the home venue of the Lobos. New Mexico was hosting #1 Arizona, led by All-Americans Sean Elliott and Steve Kerr. The Lobos built an early 25-9 lead, and the Wildcats slowly came back. Elliott had a chance to put Arizona into the lead with seconds left, but Greene blocked the shot to seal the win, the only time the Lobos have beaten a #1-ranked team. New Mexico beat #5 Wyoming a week later and climbed into the rankings at #19. They fell into a 6-10 slide, however, struggling badly on the road. They again went to the NIT, where they won two games before losing in the quarter-finals to finish the season 22-14. Greene finished his career as the leading scorer in Lobo history, with 1,745 points, though he has since fallen to seventh, and he is second in career steals, behind Scarborough. He is the only Lobo ever to surpass 1,500 points, 600 rebounds, 300 assists, and 200 steals. The Lobos went 90-48 during his four years, with four NIT appearances.
Career stats
Bold indicates team leader; * Lobo record for steals in a season