The Baltimore Ravens finished third in the AFC North with a 10–6 record and qualified for a wildcard spot. On January 3, 2015, Stewart started his first career playoff game and recorded one solo tackle, two pass deflections, and intercepted a pass by Ben Roethlisberger in the fourth quarter of the Ravens' 30–17 win against the Pittsburgh Steelers in the AFC Wild Card Round. The following week, he made two solo tackles as the Ravens lost 35–31 to the eventual Super Bowl XLIX Champions the New England Patriots.
Stewart became an unrestricted free agent after the 2014 season and did not receive an offer to return to the Baltimore Ravens. On March 12, 2015, Stewart attended a visit with the Denver Broncos and received a contract offer after he met with team representatives. The following day, he met with personnel from the Atlanta Falcons.
On March 13, 2015, the Denver Broncos signed Stewart to a two-year, $4.25 million contract that includes $2.25 million guaranteed and a signing bonus of $1.5 million. Head coach Gary Kubiak was also with the Baltimore Ravens the previous season as their offensive coordinator.
He started the Denver Broncos' season-opener against his former team, the Baltimore Ravens, and recorded four combined tackles, a pass deflection, and intercepted a pass by Joe Flacco to seal their 19–13 victory. On September 27, 2015, Stewart recorded a season-high eight combined tackles during a 24–12 victory at the Detroit Lions. He finished his first season with the Broncos with 63 combined tackles (48 solo), ten pass deflections, two fumble recoveries, and a forced fumble in 15 games and 13 starts. Pro Football Focus gave Stewart a 77.1 coverage grade, 80.4 grade for run defense, and an overall grade of 81.8 in 2015. His overall grade ranked 16th among all qualifying safeties.