The Blue Jackets' fortunes have turned around since Ken Hitchcock replaced fired coach Gerard Gallant on Nov. 22. Columbus is 6-3 under Hitchcock and has outscored opponents 21-4 during the winning streak.
Hitchcock, fired by the Philadelphia Flyers earlier this season, had his greatest success with Dallas - leading the Stars to their only Stanley Cup title in 1999 and amassing the most coaching victories in team history during his tenure from 1996-2002.
Columbus won in Dallas for the first time in franchise history. The Blue Jackets were 0-9-1 in their first 10 visits to Texas.
Norrena, a 33-year-old rookie, won his fifth straight start and has allowed two goals in his last four games, all on the road.
David Vyborny and Dan Fritsche scored for Columbus after misplays by Dallas goaltender Marty Turco.
Jason Chimera added his fifth goal of the season with 6:20 left to stretch Columbus' lead to 3-1.