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.
On November 19, 2013, the University of North Carolina sent a disassociation letter to Quinn, Marvin Austin, and Greg Little for the improper benefits taken during the their time at the university. The three athletes are prohibited from contacting current North Carolina athletes and are not allowed inside the Kenan Football Center or other athletic facilities on campus.
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, projecting 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.
In 2012, Quinn started fourteen of the Rams' sixteen games. He set career highs in tackles and sacks with 29 and 10.5, respectively. In Week 5 against the Arizona Cardinals, Quinn recorded 3 sacks, a pass deflect, and the first forced fumble of his career.
In Week 1 of 2013 versus the Arizona Cardinals, Quinn tied his career high for sacks in a game with three, causing two fumbles and was also held once by Cardinal left tackle Levi Brown in a 27–24 Rams win in St. Louis. For his efforts he was named Sports Illustrated's NFC Defensive Player of the Week for the first time. In addition he was named the Official NFL NFC Defensive Player of the Week on September 11, 2013. In Week 11 Quinn forced a fumble that was recovered for a touchdown by Chris Long and for their efforts they were named co-Sports Illustrated's NFC Defensive Players of the Week.