The Penguins, who have scored 16 goals against Winnipeg in their last two games after last month's 8-5 win, put the visiting Jets to the sword with four goals in the second period.
Neal took the spotlight with a goal in the first and two in the second, while Evgeni Malkin scored twice and had three assists to stretch his NHL-leading points total to 93.
Malkin's goals gave him 201 for his NHL career.
"To have five points is unbelievable," Malkin said. "We have a lot of talent. We have a great team. We can play physical, and we can play fast."
Tyler Kennedy also scored twice while Sidney Crosby had four assists, bringing his tally to nine in four games since returning from injury.
It was Crosby's first game in front of his home crowd in three months and his outing helped the Pens (45-21-6) rebound from Sunday's defeat to Philadelphia which ended their 11-game win streak.
Bryan Little scored twice for Winnipeg (34-31-8), who stayed four points behind Washington for the final playoff spot in the conference.
"It's frustrating," said Jets forward Tanner Glass. "At the same time, that's a great team. When you start a game with Crosby as your third-line center, it just shows you right there the pace they're going to come at you with."
Jim Slater and Tim Stapleton also scored for the Jets against Pittsburgh rookie goaltender Brad Thiessen, who made 26 stops in the win.
Winnipeg netminder Ondrej Pavelec was chased in the second period after allowing five goals. Chris Mason surrendered the final three.