Backes broke a 1-1 tie with a power-play goal at 13:09 of the third before being credited with an empty-netter at 18:49 to help St. Louis become the first team to cross the 100-point plateau in the NHL this season.
Brenden Morrow recorded St. Louis' other goal, while Ryan Miller made 16 saves to improve to 7-0-1 since being acquired on Feb. 28 by the Blues, who have won three straight and eight of their last nine games.
Eric O'Dell potted Winnipeg's lone goal, while Al Montoya allowed two goals on 25 shots for the Jets, who have lost seven of their last eight games.
2014: The Year in Fashion [PHOTOS]
LeBron James reveals his new Nike shoes