In 1981, after Charlie Waters retired, cornerback Benny Barnes was moved to strong safety and rookie Michael Downs to free safety, so Thurman became the starter at right cornerback. He registered 76 tackles, one fumble recovery and 9 interceptions (third in team history), which was second on the team to Everson Walls' 11 picks. In the season opener against the Washington Redskins, he returned an interception 96 yards for a touchdown, which was the second longest in club history. He had 2 interceptions in the 28–27 win against the Miami Dolphins. In the fifteenth game against the Philadelphia Eagles, he tied a franchise record with 3 interceptions in a single-game, helping to clinch the NFC East championship. His 187 interception return yardage in the season ranked second in club history. He had 2 interceptions in the 38-0 playoff win against the Tampa Bay Buccaneers.