As a freshman in 2008 Quinn started 12 of 13 games, recording 34 tackles (6.5 for losses) and two sacks and forced two fumbles. He was also named the ACC's Brian Piccolo Award winner as the league's most courageous player and finished third in the voting for the ACC Defensive Rookie of the Year honors.
As a sophomore in 2009 Quinn had 52 tackles and led the ACC and was 15th in the country in tackles for losses with 19.0 and was second in the league and 16th in the nation in sacks with 11.0 sacks. Additionally, he had three pass breakups and was second in the ACC and fourth in the country with six forced fumbles. For his efforts he was a First-team All-ACC selection and was a Second-team All-American by CBS. He also finished second in the ACC Defensive Player of the Year voting.
As a junior in 2010, Quinn missed the season after he was ruled ineligible by the NCAA for lying to investigators about receiving travel accommodations and jewelry.
Already in April 2010, Quinn was regarded as one of the top prospects for the 2011 NFL Draft. Despite sitting out all of his junior season, he was still projected to be a top-10 selection in January 2011. His stock slightly dropped after the combine, projectim him at No. 11 in early March. Quinn was eventually drafted as the 14th pick in the 2011 NFL Draft by the St. Louis Rams.
On July 30, 2011 Quinn signed a four-year $9.4 million contract (including a $5.3 million signing bonus) with the St. Louis Rams and arrived a day late to practice due to the birth of his first son. On September 19, 2011, Quinn recorded his first career sack against the Giants on Monday Night Football. On October 30, 2011, Quinn recorded his second sack and blocked a punt against the New Orleans Saints, earning the NFC Special Teams Player of the Week Award for his effort. Quinn ended his rookie season with five sacks, three blocked punts, and generated positive reviews for his pass rushing skills.