To find a quick answer, I've looked at the vital statistics of the recent winners during their regular seasons to see how well these squads were doing against their peers during their successful seasons.
|Total +/-||ES Goal +/-||ES Goal%||Fenwick Close||Non ES Goal +/-||ES SH%||ES SAV%|
The winners had a fair range of observable talent, but they average out a team that was ahead of their opponents by half a goal per game in the regular season, three quarters of that on ES. Their shot differential skill averages to just above 54%, which is where the best Fenwick close teams tend to be most seasons. Noticeable trend on special teams, either good or average and regular season goaltending that is typically much better than average (except for the Blackhawks).
The striking similarity is that these are all teams that managed to be 55%+ on ES goal differential, a difference that, with the average number of ES goal events for and against for a NHL team being ~320 in 82 games (about 4 per game), works out to about +30 on the year, similar to the +32.4 average observed. The exception is L.A., but they were shooting blanks that season and had a shot-control skill of close to 54% and above average save%, putting that magic 55% well in their grasp.
There does not seem to be much of a pattern on how the 55% is achieved. Detroit flat-out dominated their way to it as the best shot control team in the post lock-out era. Chicago got there by being their only peers in shot control, somewhat undermined by goaltending. Pittsburgh and Boston accomplished this by PDO dominance; Pittsburgh largely on the backs of the huge offensive advantage Sidney Crosby and Evgeni Malkin could have on a team's on ice shooting, Boston by their other-worldly save%. It should also be noted that the ordinary Fenwick teams all were on the rise and their regular season results may not truly reflect their real Fenwick talent during the playoffs. Pittsburgh became possession-dominant after a coaching change, and were 54% the next year. Boston was developing and had yet to exploit Tyler Seguin, being 53% Fenwick the next year. L.A. had both a coaching and personnel change that put them well above 55% in shot control.