The N.F.L.’s 32 clubs passed a rule change on Tuesday to ensure that both teams would possess the ball at least once in overtime of postseason games. The measure comes months after Kansas City won a divisional round playoff game against the Buffalo Bills, who were not given a chance to score in overtime.

The change in the league’s overtime rules was their first since 2010, when clubs voted to allow teams that scored a touchdown on the opening possession of overtime in a playoff game to win. (Before that, the team that scored first in any way in overtime won.) The rule, which by its nature gave an advantage to the team that won the overtime coin toss, was extended to the regular season in 2012.

Since 2010, there have been 12 postseason overtime games, and the team that won the coin toss preceding overtime went on to win 10 of those 12 games. Seven of those 10 wins came on a first-drive touchdown.