The Stanley Cup final format is a best 4 out of 7. The team that wins 4 games first is the winner. The fewest number of games that could be played is 4 and the highest number of games that could be played is 7.
The Colorado Avalanche took the 1996 Stanley Cup Finals series in 4 straight games against the Florida Panthers
This doesn't exactly answer the question, but Steve Brule of New Jersey managed to win the Stanley Cup with 0 games played in the regular season career at that point (1 playoff game only in 2000 when the Devils won the cup)
I'm pretty sure that it is just the NHL decided who are the best refs (most experienced, fewest missed calls, most times reffing a Stanley cup etc.)
The Canucks vs Rangers Stanley Cup Finals took place in 1994.
The Penguins won the 2009 Stanley cup in 7 games against the Red Wings
The Stanley cup finals have only went up to 7 games and never past.
The last time the Montreal Canadiens took home the Stanley Cup was in 1993. Coincidentally, 1993 was also the 100th anniversary of the awarding of the Stanley Cup (first Stanley Cup awarded in 1983).
The Chicago Blackhawks won the 2013 Stanley Cup in 6 games against the Boston Bruins.
41 regular season games or 1 Stanley cup final game.