The Houston Texans finished atop their division with a 12–4 record. On January 5, 2013, Quin made three pass deflections and two solo tackles during a 19–13 victory against the Cincinnati Bengals in the AFC Wildcard Game. The following week, he made five combined tackles in the Texans' 41–28 loss to the New England Patriots in the AFC Divisional Round.
Quin became an unrestricted free agent after the 2012 season and was intent on staying with the Houston Texans. Many analysts cited Quin as the Texans' top free agent priority. The Texans general manager Rick Smith decided against the franchise tag and Quin's agent claimed Quin never received an offer from the Texans. On March 12, 2013, it was reported that Quin was visiting the Detroit Lions immediately after the free agency period began.
On March 13, 2013, the Detroit Lions signed Quin to a five-year, $23.50 million contract that includes $6.25 million guaranteed and a signing bonus of $5.25 million.
He started in the Detroit Lions' season-opener against the Minnesota Vikings and recorded two combined tackles, a pass deflection, and intercepted a pass by quarterback Christian Ponder in their 34–24 victory. The following week, he collected a season-high six solo tackles and deflected a pass during a 25–21 loss at the Arizona Cardinals in Week 2. In Week 4, he made a season-high two pass deflections, a solo tackle, and intercepted a pass by Jay Cutler during a 40–32 victory against the Chicago Bears. On December 31, 2013, the Detroit Lions fired head coach Jim Schwartz after finishing third in the NFC North with a 7-9 record in 2013. He finished the season with 57 combined tackles (44 solo), eight pass deflections, three interceptions, a sack, and a forced fumble in 16 games and 16 starts. In his first season with the Lions, Quin earned an overall grade of +7.4 from Pro Football Focus and ranked tenth among all qualifying safeties.