If anyone is looking for a team having an edge in one PO series due to coaching, I am not sure if there is any clearer example than our PO series against the Atlanta Thrashers in 07'. Tom Renney had us playing an extreme puck possession game.
The Thrashers simply had -- a loaded -- roster. Prime Hossa and Kovalchuk. Slava Kozlov was a PPG and they added Keith Tkachuk who still was a top PF in the NHL.
But Bob Hartley employed exactly the same system designed to beat the trapping teams before. Their Ds were not allowed to be fancy with the puck. Their centers' prime role was to balance the team and win board battles. At center, they had Slava Kozlov, Holik, Rucchin and Erik Belanger IIRC. Guys like Shane Hnidy, Garrnet Excelby and the likes were brought in to clear the crease. They chipped pucks out of their own end to isolated forwards high up ice, we won it back and acted in concert as a team.
I think Atlanta only scored 6 goals over 4 games, Hossa, Kovalchuk, Kozlov and Tkachuk combined for 1 goal. We dominated them completely over 240 minutes.