With two more points, Modano can tie Phil Housley's record of 1,232. He scored on the power play in the second period and assisted on Mike Ribeiro's third-period goal.
The 37-year-old Modano, from Livonia, Mich., has played his entire career with the franchise since the Minnesota North Stars made him the top overall pick in the 1988 draft. He made his NHL debut in the 1989-1990 season.
Shane Doan, Radim Vrbata and Daniel Carcillo scored for Phoenix, which has lost five straight at home.
Dallas goalie Mike Smith stopped 28 of 31 shots to earn his second win of the season. Sergei Zubov, Niklas Hagman and Jere Lehtinen also scored for the Stars
Phoenix goalie Alex Auld allowed a soft goal early in the game when he missed Zubov's weak shot from the right point. Doan tied it shortly afterward when he redirected Ed Jovanovski's shot from the left point at 12:20.
Notes: Modano had his first two-point game of the season. ... Doan's goal was the 200th of NHL career, including seven with Winnipeg before the franchise moved to Phoenix in 1996. ... Ribeiro also had two assists, for his first three-point game of the season. ... Hagman's goal was short handed.