Last Team to Tank a Season and Win a Super Bowl a year or two after?

Saints went from 3-13 in 2005 to NFC title game in 2006
Not to downplay the accomplishment because they could have easily gone 11-5 if the week 17 game gave them anything to play for that season, but the 2006 NFC was one of the worst seasons-by-conference in NFL history, and certainly so since the 2002 realignment. From 2002-2019 (the four division, six qualifier era), a 10-win team has never been a 2-seed, except for that year’s Saints. This can be reviewed and confirmed year over year here: https://www.pro-football-reference.com/years/2006/index.htm

It was so bad Rex Grossman’s Chicago Bears represented the NFC in the Super Bowl. They lost by two scores.