The Red Wings controlled the puck for the first minute-plus of the 3-on-3 period before the Stars gained control and moved into the offensive zone. John Klingberg, who scored the other Dallas goal, passed up a couple of opportunities to shoot and sent the puck to Dickinson, who beat Thomas Greiss from the high slot.
''I saw he probably thought that I was going to shoot it so I was going to take him out,'' Klingberg said. ''I actually lost the puck when I went to shoot myself, but after that (Dickinson) found a way to get open.''
The former longtime Central Division rivals played as division foes for the first time since 1997-98, again in the Central, after the NHL had to realign as part of adjustments in scheduling for the coronavirus pandemic.
Detroit dropped a fifth straight game in Dallas but gained a point for the first time that stretch. The Red Wings are winless in four of their past five games this season.
Anton Khudobin stopped 20 shots to improve to 3-0. Greiss also had 20 saves.
The Stars had their first two games called off because of COVID-19 protocols before beating Nashville twice while tying an NHL record with eight power-play goals in their first two games.
The only goal in regulation for the Stars was again with the man advantage, making Dallas the first NHL team with at least nine power-play goals through the first three games since Vancouver in 1983-84.
Dallas trailed for the first time this season when Vladislav Namestnikov scored his first goal for the Red Wings, catching Khudobin unprepared and slipping a soft backhander between the goalie's legs on a pass from Taro Hirose in the first period.
''Maybe scoring the goal is a weight off his shoulders,'' coach Jeff Blashill said. ''He's definitely somebody who feels that he's hard on himself. We just talked about just playing and not worrying about points and goals. When you're a forward you worry about that stuff, and so it was good for him to get it.''
The Stars came in 8 of 12 on the power play in the first two games but generated just one shot on their only opportunity in the first period before converting four seconds into their second chance.
Klingberg's shot from just inside the blue line was set up by the penalty Justin Dowling drew when a nice move in the neutral zone gave him a run at Greiss. Filip Hronek was called for slashing on Dowling's shot attempt.
Pavelski won the ensuing faceoff and Denis Gurianov fed the puck to Klingberg, whose shot through traffic appeared to have been tipped but went over Greiss' left shoulder untouched. Pavelski's assist was his 800th career point.
Klingberg has a goal and five assists after the high-scoring defenseman tied his career high with three assists in the opener coming off a strong performance in the playoff bubble in helping Dallas reach the Stanley Cup Final.
''You go back to the playoffs in Edmonton and Klinger was our best defenseman,'' coach Rick Bowness said. ''He wants the ball right now. He was that way in the playoffs. He wants to be out there in key situations.''
ANOTHER SIDELINED STAR
Roope Hintz joined captain Jamie Benn on the inactive list for Dallas with a lower-body injury. Hintz had five points in the first two games with one goal and four assists, all on power plays. Benn missed his second consecutive game after his right leg buckled awkwardly during a collision in the opener.
Another forward, Joel Kiviranta, is on injured reserve with a lower-body injury sustained in practice between the first two games. High-scoring forward Tyler Seguin isn't expected back into April after offseason hip surgery.
''We've been through a lot as a group,'' Dickinson said. ''We've had guys shuffle in and out often. You saw it in the bubble. Guys had to step up at key times.''
The Red Wings remain without forwards Adam Erne, Robby Fabbri, Sam Gagner and Filip Zadina and defenseman Jon Merrill because of COVID-19 protocols. Erne and Fabbri have been out five games, while Gagner, Zadina and Merrill have missed three apiece.
These teams meet again Thursday in Dallas.
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