The Penguins ended the Stars' four-game winning streak and handed Dallas only its fourth setback of the season.
Neal, a former member of the Stars, tied the game with 2:04 to play in the second period and gave the Penguins the lead 7:19 into the third. The final Pittsburgh goal was scored on a penalty shot by Matt Cooke at the midway point of the closing period.
The Penguins won their second in a row and moved one point in front of Dallas for the best record in the NHL.
This was the third game in a four-game road trip that was expected to test the Stars, who have gotten off to a surprisingly good start this year. Dallas won the first two stops in the trip, downing Carolina and Washington. The journey ends Saturday in Detroit.
The lone Dallas goal came from Eric Nystrom in the opening period.