Dallas has won three consecutive games and has earned points in eight of its past 11 outings.
Hanzal's deciding goal came as he set a screen in front of the net and redirected a shot from the point by Julius Honka past New York goaltender Henrik Lundqvist. Esa Lindell also got an assist on the play.
It was the only score on the power play in eight combined man-advantage chances for the two teams, five of them for Dallas.
The Stars forged a 41-32 advantage in shots on goal, while New York had more hits than Dallas (30-26) and more blocks (28-13).
The Rangers have lost five of their past six games.
Dallas outshot the Rangers 21-9 in the first period, but New York had the one shot that counted the most. David Desharnais deflected a shot on goal, scooped up his own rebound and tucked the puck in behind Dallas goaltender Ben Bishop for a 1-0 Rangers lead at the 17:55 mark. Vinni Lettieri and J.T. Miller were given assists in the goal.
The Stars tied the game on a goal by Tyler Seguin with 5:16 to play in the second period. Seguin's slap shot from the top of the circle bounced off the post and New York goalie Henrik Lundqvist's blocker.
Jason Spezza and Alexander Radulov assisted on the tally, which was Seguin's 26th of the season, tied for seventh best in the NHL.
Lundqvist made 39 saves, while Bishop stopped 31 shots in the win.
Dallas returns to the ice on Thursday in Chicago while the Rangers head back to the Big Apple for games Wednesday and Friday against Boston and Calgary, respectively.
--Field Level Media
NY Rangers | Dallas | |
David Desharnais 1 | Points | Martin Hanzal 1 |
David Desharnais 1 | Goals | Martin Hanzal 1 |
Vinni Lettieri 1 | Assists | Julius Honka 1 |
N/A | Power Play Goals | Martin Hanzal 1 |
N/A | Short Handed Goals | N/A |
Henrik Lundqvist .951 | Save Percentage | Ben Bishop .969 |
Henrik Lundqvist 39 | Saves | Ben Bishop 31 |
Team | Shots | Goals | Power Play | Penalty Kill | Penalty Mins | Face Offs Won |
NY Rangers | 32 | 1 | 0-3 | 4-5 | 10 | 21 |
Dallas | 41 | 2 | 1-5 | 3-3 | 6 | 30 |