The 2007 Red Sox - had 96 wins and then went 11-3 in the playoffs. They might have been the best Sox team of the 4 who won in this century.
The 1976 Patriots -
https://en.wikipedia.org/wiki/1976_New_England_Patriots_season
Went 11-3 but had a no show game in Detroit that came back to haunt them as they wound up playing Oakland on the road in the playoffs and that didn't end well.
View: https://youtu.be/UjQ3mVZQl1U?t=15
The 86 Celtics - lost ONE game at home during the regular season.
The 1971 Bruins might have been the best team they ever iced but lost to an aging Montreal team in the first round with a rookie goalie. Bobby Orr didn't have many bad games in his career but Game 2 against Montreal in 1971 may have been his worst.
View: https://www.youtube.com/watch?v=TGjpo8CxqXY
To me, the 2004 Red Sox will be #1 until I die. They were faced with 4 elimination games after losing Game 3 of the ALCS 19-8 and ran the table.
The following year the White Sox erased an even longer drought than the Red Sox and couldn't even get on the cover of SI the following week let alone TIME.
I would put the Bruins 2011 Cup team second.
In 4 playoff series, they had to win Game 7 three times including once on the road in Vancouver and they had to eliminate Montreal in round 1 after losing the first 2 games at home.