The Penguins, hoping to fulfil expectations this season after consecutive first-round play-off losses, knocked off Philadelphia in the season opener and followed it up with another dominant triumph on the road against New York.
"It's a good start," Penguins captain Sidney Crosby said after registering his first point of the year on an assist in the first period.
"We've done a lot of good things the last couple games, played some good periods of hockey. You just want to keep that going and keep getting better."
The game had opened with fireworks as New York's Arron Asham and Pittsburgh's Turner Glass dropped their gloves and fought just two seconds into the match, but the fight went out of the Rangers for most of the night.
Pittsburgh tallied three goals in the first period and held a 5-1 advantage in the third before the Rangers rallied.
Neal scored in the first and third periods to take his tally to three goals for the season, while reigning Hart Trophy winner Evgeni Malkin added three assists.
Goaltender Tomas Vokoun, making his debut with the Penguins after being traded from the Washington Capitals, had 31 saves to outplay New York's Henrik Lundqvist.
Lundqvist, last year's Vezina Trophy winner, allowed four goals on 18 shots and was pulled in the second period.
It was the first time he had been pulled due to performance since 2011 and was a second straight poor outing after he surrendered three goals in a loss to Boston on Saturday.
"Personally, it was a tough night," Lundqvist said. "I really don't have an explanation other than we just have to work harder and keep getting better."
Winless New York got goals from Taylor Pyatt and Rick Nash in the third to briefly pull within 5-3 of Pittsburgh but it did not last as Kris Letang extended the advantage late on.
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