Alex Burmistrov and Andrew Ladd scored consecutive goals in the second period, lifting the Jets into a 4-2 lead.
Chris Mason turned aside 33-of-36 shots on a night when Jets fans honored Anaheim's Teeme Selanne, one of the NHL's all-time leading scorers with 647 career goals.
The likely future hall-of-famer began his career as a draft choice of the former Jets -- now the Phoenix Coyotes -- and scored rookie record of 76 goals in the 1992-93 season.
Saturday's contest marked Selanne's first game in Winnipeg since 1996.
Dan Ellis made 26 stops for Anaheim.