Morrow, who signed a six-year, US$24-million contract extension last month, was selected the team's fifth captain since it moved to Texas in 1993.
The 27-year-old left winger rewarded the Stars with his first goal of the season that gave them a 2-0 lead early in the second period. Morrow also assisted on Lindros' goal that gave the Stars a two-goal cushion with 2:48 remaining in the game.
Lindros, who has endured several concussions during his career, signed a one-year deal with the Stars in the off-season after playing in only 72 games the past two seasons.
Niklas Hagman scored a short-handed goal for Dallas in the first to open the scoring.
Centre Travis Zajac had a power-play goal at 8:33 of the second to pull New Jersey to 2-1 in the rematch of the 2000 Stanley Cup Finals.
However, the Devils could not complete the rally after defeating defending Stanley Cup champion Carolina 4-0 on Friday.
Dallas goalie Marty Turco had 19 saves to win his second straight to start the season.
New Jersey's Martin Brodeur, who tied Terry Sawchuk on the all-time wins list Friday night, had 28 saves.
Jeff Halpern was whistled for a holding penalty at the 11:07 mark of the first period. But Dallas overcame the penalty 41 seconds later when Stu Barnes hit Hagman, who beat Brodeur in the slot.
The Stars extended their lead to 2-0 in the second. Mike Ribeiro was behind the net where he passed the puck to a wide-open Morrow at 4:44 of the second.
Dallas continued to struggle on the power play, going 0-for-5 - including a missed chance when they had a 5-on-3 advantage for 58 seconds late in the first. They have not scored in nine power-play chances this season.
Notes: Dallas will not play at home again until Oct. 20 against Chicago. The Stars open a four-game road trip with consecutive games next week against the Los Angeles Kings. ... New Jersey C John Madden needs one point for 200 in his career. ... The Stars improved to 7-0-1 in their last eight home openers. They are now 10-2-1 in home openers since moving from Minnesota in 1993. ... The Devils will have four days off before their home opener Thursday against the Toronto Maple Leafs. ... Dallas improved to 2-4-0 against New Jersey since the 2000 Stanley Cup Final.