Good fortune carried them. Their -36 goal differential is the worst by a playoff team since the Whalers were -36 in 1991-92, when 16/22 teams made the playoffs.
This is a pretty myopic way of looking at things. The Caps in the first half of the season dealt with the ineffective and then loss of their top two centers, multiple injuries, adjusting to a new coaching staff and marginal goaltending play. Around February they settled in with Lindgren as their starter, traded Kuznetsov, LTIRed Backstrom, and found some roster stability. They were a middle of the pack team the second half of the season.
Good fortune did not carry them. Doing well in close games and being able to hold leads carried them.