Viktor Fasth made 24 saves for the shutout - his fourth of the season - and the Ducks claimed a divisional crown for the first time in six years.
The Vancouver Canucks also sealed their division, beating the Chicago Blackhawks 3-1 to become Northwest kings.
Daniel Sedin had a goal and an assist, while Zack Kassian and Jannik Hansen also scored for the Canucks.
Dustin Jeffrey had a goal and an assist as the Pittsburgh Penguins made it seven wins in a row by seeing off the Ottawa Senators 3-1.
Jarome Iginla and Tyler Kennedy were also on the scoresheet for the Penguins, while Patrick Wiercioch got the Senators on the board.
Aaron Gagnon and Antti Miettinen scored for the Winnipeg Jets as they saw off the Buffalo Sabres 2-1 and Johan Franzen netted twice in