Crosby, who entered the night with only four penalty minutes this season, squared off against Matt Niskanen at 12:33 of the second period while Pittsburgh trailed by three goals.
That was one of four bouts in the first two periods.
"Morrow went after Letang there, so it was just a response, sticking up for Tanger," Crosby said. "I don't think you really need to fight him there, but that's all it was."
Niskanen was at first stunned that Crosby challenged him. Niskanen quickly gathered himself and held his own against the Penguins captain.
"I never saw that coming," Niskanen said. "We were up 4-1, he was trying to get the team going a little bit, he asked me to go, and we went. I got him hard once in the helmet, if that counts. But he's very strong on his skates and he probably had the upper hand a little bit."
Dallas had been 0-4-1 in the previous five matchups with Pittsburgh. The Stars beat the Penguins for the first time since March 2, 2003.
But the Crosby-Niskanen fight was the talk of both locker rooms.
"You've got to give credit to Sidney trying to inspire his group," Stars coach Marc Crawford said. "I like the way Matt Niskanen got in there, he certainly will be on a lot of highlight tapes tonight."
Kennedy and Matt Cooke scored for the Penguins, who opened a stretch of three games in four nights against Western Conference opponents.
Brent Johnson stopped 24 shots for Pittsburgh, which has lost four of five (1-3-1). Johnson went 5-0-1 in his first six starts this season and was coming off his 14th NHL shutout in his previous outing Saturday at Carolina.
Dallas dropped the first three of a season-high, six-game homestand, but has won the last two.
The Stars got off to a fast start, holding a 12-4 shots advantage in the first period and gaining the early edge when Robidas' shot from the right point got past Johnson at 3:51.
Richards' one-timer from the left circle off a setup by Neal made it 2-0 at 7:57 of the first.
The Stars got another lift when they killed off a 5-on-3 advantage that lasted 1:37 later in the period.
"It was a big momentum swing there," Niskanen said. "The guys did an awesome job of keeping them on the outside."
Kennedy's backhander off a faceoff sneaked past Lehtonen to make it 2-1 at 6:20 of the second, but Ott popped a shot into an open net off Robidas' setup to restore the two-goal advantage at 10:52.
Eriksson was awarded his first career penalty shot at 11:51 of the second when he was hauled down by Alex Goligoski on a breakaway. Eriksson faked Johnson out of position and tapped a backhander into an open net to make it 4-1.
"I actually thought about doing that move from the start," Eriksson said. "I did it once in Vancouver two years ago [in a shootout] and it worked, and today it worked again."
The Penguins thought they had cut the deficit to 4-2 at 16:52 of the second period on Mike Comrie's redirected goal. After a video review, officials ruled that Comrie guided the puck into the net with his glove and waved off the goal.
Cooke's goal at 15:36 of the third period made it 5-2.
The Penguins got reinforcements on defense with the return of Letang (hand and wrist), Zbynek Michalek (shoulder) and Goligoski (undisclosed injury). Pittsburgh C Evgeni Malkin was also back after sitting out Saturday's win over Carolina due to a bruised knee. C Jordan Staal will be out until the middle of December (broken hand). ... Elvis Andrus and Jorge Cantu from the AL champion Texas Rangers were in the crowd and were pictured on the big screen during a break in the second period. They were loudly cheered, and saluted the fans with the team's signature antlers sign.