Neal's 14th goal this season started the scoring at 5:58 of the first period, his 15th gave Dallas a 4-2 lead at 13:29 of the second, and he assisted on Andrew Hutchinson's first goal at 18:02 of the third.
Goalie Marty Turco was credited with 35 saves on 38 shots in the Stars' season-high fourth straight win. They have four straight for the first time since Feb. 22-28 of last season.
Columbus's Kristian Huselius had a goal and an assist. Both Jared Boll and Fedor Tyutin also scored.
Backup goalie Wade Dubielewicz yielded four goals on 23 shots after starter Steve Mason gave up three goals on eight shots in just 10:43 of ice time for the Blue Jackets, who had won two in a row.