Lundqvist's brother, Joel, was in the Dallas lineup, making it the third matchup of twins in NHL history. Rich and Ron Sutter were the last to meet up March 14, 1994. Patrik and Peter Sundstrom played against each other 18 times. Joel Lundqvist was called up from Iowa of the AHL earlier Thursday after Stars centre Mike Modano was placed on injured reserve (hip-groin), retroactive to Dec. 4.
Rachunek scored one short-handed goal and another on a power play for the Rangers, who were outshot 45-20 and had to survive 11 power plays.
Fedor Tyutin added a short-handed, empty-net goal for the Rangers with 1:03 remaining.
Cullen gave the Rangers a 2-1 lead 57 seconds into the second when his centring pass bounced in off the leg of Stars rookie goaltender Mike Smith, who made 15 saves in his sixth NHL start.
Cullen made it 3-1 at 1:44 of the third when his shot from the slot got through Smith's pads, but Philippe Boucher notched a power-play goal a minute later to pull the Stars to within a goal.
Rachunek's power-play goal with 4:03 left extended the Rangers' lead to 4-2.
Sergei Zubov had a first-period, power-play goal for Dallas, which lost for the third time in four games.
The Rangers couldn't stay out of the penalty box in the first, leading to five Stars power plays and Dallas' 16-4 edge in shots.
Dallas broke through at 16:24 of the first period when Zubov cashed in on a 5-on-3 advantage with a one-timer from between the circles.
Less than a minute later, Dallas' Eric Lindros was checked into the boards and his stick became lodged between panes of plexiglass. While Lindros tried in vain to work the stick loose, the Rangers took off on a 2-on-1 short-handed break that Rachunek finished off at 17:11 after a setup by Adam Hall.
Notes: Rachunek scored his first two goals of the season and first since March 25, 2004, finding the net on the Rangers' third shot . . . Modano missed his fifth straight game. The earliest he could return is Saturday at Los Angeles . . . Henrik Lundqvist's previous career high for saves was 38, twice last season as a rookie.