Matt Calvert added a goal for the Blue Jackets, 5-0-2 in their last seven road games to move closer to playoff contention.
Brad Richards notched his 24th goal and Kari Lehtonen stopped 37 shots for the Stars, 2-6-1 in their last nine.
Nash gave Columbus a 2-1 advantage at 6:33 of the second, taking a pass from Jakub Voracek, skating in alone and sending a backhander past Lehtonen for his team-high 26th of the season and 15th of his career against Dallas.
Mason came up with a big save on a rebound attempt by Dallas' Steve Ott with over 7 minutes left, with Mason stretching his left pad to steer the shot aside.
The Stars went in front at 4:36 of the first period on Richards' power-play goal, a sharp-angle attempt from the right boards that was more of a pass than a shot.
Dallas wasn't ahead for long as Calvert drew Columbus even at 1 on a rebound 1 minute and 4 seconds after Richards' goal.
The Stars were fortunate to escape the first period in a tie after being outshot 18-6 and losing 17 of 23 faceoffs.
Stars defenseman Nicklas Grossman left the game in the first period with a lower-body injury and did not return. Grossman starts with Stephane Robidas on Dallas' top defensive pair, and the Stars had to shuffle their defensemen to compensate for Grossman's absence.
Notes: Columbus RW Derek Dorsett sustained a head injury in Friday night's home win over Colorado and remained in Columbus. ... Veteran forward Jason Williams, signed on Saturday as a free agent for the rest of the season, made his Stars debut, playing LW on the fourth line. Williams was brought in to cover for injuries to C Adam Burish (broken orbital bone), RW Krys Barch (scratched cornea and fractured orbital bone), RW Ray Sawada (separated shoulder and broken nose), C Jamie Benn (shoulder) and C Toby Petersen (leg). Petersen is practicing with the team and is expected to be activated next week.