Boswell made his NFL debut on October 12, completing all three of his extra points and making a 47-yard field goal attempt in a Monday night victory over the San Diego Chargers. He connected on the longest debut conversion in team history, besting Todd Peterson’s record of 46. On October 18, the following week against the Arizona Cardinals, Boswell was 4-for-4 on field goals including kicks of 48, 49, and 51 yards, earning him AFC Special Teams Player of the Week honors. He is the first Steeler in team history to make three 47+ yard field goals in one game. On November 8, Boswell kicked three field goals, including the game-winner and three PATs against the Oakland Raiders., albeit missing his first field goal season-to-date. On November 15, Boswell kicked three field goals against the Cleveland Browns. His 14 field goals is tied for fourth among rookie/first-year players in team history, just behind Jeff Reed (2002, 17). On November 29, Boswell kicked three field goals against the Seattle Seahawks. On October 25, Boswell kicked two field goals against the Kansas City Chiefs. On December 6, Boswell kicked three field goals against the Indianapolis Colts. On December 13, Boswell kicked four field goals against the Cincinnati Bengals. On December 20, Boswell kicked two field goals against the Denver Broncos. He tied a franchise record for the most consecutive games played while scoring at least 10 points, tied with Gary Anderson (1985). He also passed Kris Brown for the most made field goals by a rookie or first-year player in the history of the franchise with 29. He also set Steelers’ records for rookie/first-year kickers for points in a season with 113 and field goal percentage at 90.6. On January 7, 2016, Boswell won AFC Special Teams Player of the Month for the month of December.
On January 9, 2016, Boswell kicked four field goals in an 18–16 win in the AFC Wild Card game against the Cincinnati Bengals. He successfully kicked a 35-yard game-winning field goal with less than 20 seconds remaining in the game. He set an NFL record for the most field goals by a rookie/first-year player in a playoff game. His four field goals also tied for the most in Steelers playoff history (Gary Anderson in the 1989 Wild Card Round). He also became the youngest kicker to make four field goals in a postseason game. On January 17, 2016, in a loss against the Denver Broncos during the Divisional Round of the playoffs, Boswell tied a franchise record with seven total field goals completed in the post-season.